The 22-year-old starred for the Dutch club last season to help them win the Eredivisie and also reach the Champions League semi-finals.
He scored 12 goals in all competitions, including important strikes against Real Madrid and Juventus on the European stage.
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Journalist Jorge Nicola claims Neres turned down the chance to move to the Premier League when Man United came calling to instead remain with Ajax.
He is also thought to have accepted a new contract offer from the Dutch club which will see him become their second highest-paid player behind Daley Blind.
Marc Overmars, Ajax’s director of football, reportedly played an instrumental role in getting Neres to stay.
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The Eredivisie champions have been gutted this summer with Matthijs de Ligt and Frenkie de Jong both leaving, while there has been speculation over Donny van de Beek possibly moving to Real Madrid.
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talkSPORT.com round up all the latest transfer news and football gossip from Tuesday’s papers and online…
Paul Pogba will push to leave Manchester United this summer, but his proposed move to Real Madrid will only happen if the Red Devils lower their £160m price tag. (Daily Telegraph)
Liverpool have joined the race for Ajax’s Brazilian forward David Neres. The 22-year-old is valued at £35m. (The Sun)
Ajax’s in-demand 19-year-old defender Matthijs de Ligt has rejected a £60m move to Manchester United. (Daily Star)
United are ready to kick off their summer transfer overhaul by signing Juventus forward Paulo Dybala, and have made contact over an £85m swoop for the Argentine. (Calciomercato)
Gareth Bale has been told he is not wanted at Real Madrid in a face-to-face meeting with coach Zinedine Zidane, but remains adamant he wants to stay at the club. (Daily Mail)
Anthony Martial faces a battle to convince Ole Gunnar Solskjaer he has a long-term future at Manchester United. (Daily Mail)
But other reports claim Solskjaer will listen to offers for Martial this summer because of his bad attitude in training. (The Sun)
Manchester City are closing in on a deal to sign Sporting Lisbon midfielder Bruno Fernandes, with the club set to pay between £50m and £60m for the 24-year-old Portugal international. (Sky Sports)
Napoli manager Carlo Ancelotti has refused to rule out a move for Tottenham defender Kieran Trippier, after the England international’s wife was reportedly spotted looking for schools in Naples – FULL STORY
Newcastle United forward Ayoze Perez forward is also a target for Napoli. (Northern Echo)
Tottenham and Everton are both eyeing 23-year-old Real Betis central midfielder Giovani Lo Celso. (The Sun)
Bournemouth winger Ryan Fraser is open to joining another Premier League club this summer, with Arsenal, Tottenham, Chelsea and Newcastle reportedly keen on the 25-year-old. (Daily Mail)
Former Arsenal manager Arsene Wenger has rejected a second offer to take over at Fulham, having first turned down an approach from the Cottagers in November before they appointed Claudio Ranieri. (Daily Mail)
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Ajax are through to the Champions League semi-final after despatching Juventus in style.
The Dutch giants dumped Cristiano Ronaldo and co out of the competition thanks to a 3-2 aggregate scoreline, which had neutrals across Europe celebrating.
But while it represents a magnificent for both Ajax and European football, proving the game’s modern elite can be beaten when it matter, it feels like it could be this side’s last hurrah.
The collection of wonderkids and experienced aces may be broken up in just two months times as clubs across Europe get ready to raid Amsterdam.
Frenkie de Jong, the classy midfielder, has already sealed his transfer, having penned a move to Barcelona on July 1, which is no surprise given his astonishing ability which saw him, on occasion, embarrass Ballon d’Or winner Luka Modric in the Round of 16 victory over Real Madrid.
But where will there other heroes be going when the transfer window opens? Oddschecker.com have provided the latest odds.
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So how would Liverpool cope with his departure. talkSPORT.com looks at how Liverpool *could* line up next season.
RELEASING HENDO (4-3-3)
On Tuesday night, Jurgen Klopp apologised for playing Jordan Henderson out of position for a year-and-a-half while Liverpool captain.
The midfielder has operated in a deep role for club and country, almost like a No.6 just sitting In front of the back four. However, it was his lung-bursting runs and attacking play which earned him a £20million move from Sunderland in 2011.
With Fabinho and Neves able to interchange between attacking and defensive transitions for the Reds, the England international can bomb on and join the attack, with Naby Keita and Alex Oxlade-Chamberlain fantastic alternatives from the bench.
Fabinho’s versatility means he can drop into the ‘false full-back role’ to cover Andy Robertson and Trent Alexander-Arnold when they maraud forward. By dropping alongside the centre-halves when Liverpool are in possession, the Brazil international would allow the wingers to cut inside and create space on the overlap for the full-backs on the outside.
WING WIZARDS (4-2-3-1)
Callum Hudson-Odoi’s remarkable rise at Chelsea is eerily similar to that of David Neres of Ajax in that both men have faced adversity head on, despite their tender years.
Maurizio Sarri’s reluctance to use the 18-year-old England international had led to rumours of a move away, while Neres was not guaranteed a starting place in Amsterdam until February of this year – remarkable considering he scored 14 goals and registered 13 assists last season.
Both play with a direct and fearless style which make them nightmares for defenders to stop and Liverpool’s relentless pressing and counter-attacking style would be perfect.
With Mohamed Salah using his pace in behind to stretch teams, the mercurial Roberto Firmino would be able to exploit the spaces in between defence and midfield.
Ajax are such a fantastic team to watch. Honestly I can see so much of 17/18 Liverpool in their game. The relentless pressing and quick short passing dominate the game soooo much. They have built a fantastic team capable of challenging anyone. Also what a goal Neres.
David Neres is a player we should be targeting if we want a flexible forward. High level of possession regains in the opponents final third, dribble, & has a solid GA. Could grow into a star player at Liverpool under Jürgen.
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Neres would provide solid cover and competition for Liverpool stars Sadio Mane, Roberto Firmino and Mohamed Salah, as he can play in multiple attacking positions.
Despite signing Xherdan Shaqiri from Stoke last summer, Anfield chief Jurgen Klopp has been reluctant to rest his front three throughout a campaign in which they continue to challenge for both domestic and European honours.
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Dortmund are on the lookout for a replacement for Chelsea-bound winger Christian Pulisic.
And PSG could appeal to Neres, who would be playing alongside Brazil team-mates Thiago Silva, Marquinhos and Neymar.
Neres’ form saw him receive a first call-up to the Brazil national team last month and he made his debut as a substitute against the Czech Republic.