The Blues had a £19million bid for the striker rejected last summer, but are confident of closing a £23million deal with the Brazilian side, according to The Sun.
Chelsea owner Roman Abramovich is desperate to bring in the 19-year-old striker this summer.
A Chelsea source told The Sun: “Roman is ready to get personally involved to clinch the signing of Neymar.
“He’s aiming to talk with him next month to prove how much he is wanted.”