Neres has been attracting the attention of top clubs from across Europe after ripping up the Eredivisie this season.
The 22-year-old, with eight league goals and 11 assists to his name, has been watched by Borussia Dortmund and Paris-Saint Germain as well as Everton, Liverpool, United and Chelsea.
But now Arsenal and Everton have moved ahead in the race after both clubs had talks with Ajax, according to one report yesterday.
The report, from the Daily Telegraph, says the versatile Neres is likely to cost around €40million (£34.5m).
The Brazil international, who equalised in Ajax’s 1-1 Champions League draw against Juventus on Wednesday, is primarily a right winger but can also play on the left wing or as an attacking midfielder.
Borussia Dortmund had a bid for Neres rejected in January and will try again to take him to Germany if they lose Jadon Sancho at the end of the season.
Liverpool boss Jurgen Klopp is keen to add more to his attack this summer with fans concerned about the lack of depth in attack.
Everton boss Marco Silva, though, is determined to steal a march and thinks the lure of first-team football from the off could swing things in the Toffees’ favour over their Premier League rivals.