The 18-year-old, who will see his current deal expire next summer, has been in negotiations with the Catalan club over an extension since his agent Jorge Mendes flew over to Spain for talks last week.
One report had suggested that Barca were forced to put contract talks on hold, but according to journalist Fernando Polo, cited by Fabrizio Romano, Fati is edging closer to agreeing a new five-year deal.
Negotiations are believed to be in the final stages and both parties are now completing the necessary paperwork before they can announce the deal, which is set to include a €1bn (£847m) release clause.
Romano added that Barcelona have always been 'optimistic and confident' that the contract would be signed soon, after positive talks were held with the player's agent Mendes.
Fati, who has been linked with both Manchester City and Manchester United, recently returned from a long-term knee injury and scored his 15th goal for the senior side in the 3-1 victory against Valencia on Sunday. body check tags ::