The Press Association, as quoted by the Daily Star, is reporting that the Blues are keen on a deal to bring Neres to Stamford Bridge after missing out on Luka Jovic, who is set to join Real Madrid.
The same story says that Chelsea FC are pressing ahead with their plans for the summer transfer window because they are hopeful of having their Fifa transfer ban overturned by the Court of Arbitration for Sport.
According to the same story, Chelsea FC are now keen to seal a move for Neres this summer.
The 22-year-old has been in good form for the Dutch side this season and has scored eight goals and made eight assists in 29 league games so far this term.
He also netted twice in the Champions League to help Ajax to reach the semi-finals.
Chelsea FC are currently preparing for their Europa League final showdown against Arsenal in Baku on 29 May as they aim to end the campaign on a positive note.
The Blues finished in third place in the Premier League table to secure their spot in the Champions League for next season.
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