The Catalan giants have been working to sign the 18-year-old to a fresh deal, as his current terms at Camp Nou are due to expire next summer, although the club can activate a two-year extension.
However, according to Mundo Deportivo, Barcelona have now reached an agreement in principle with the Spain international, and an announcement is expected 'in the coming days'.
The report claims that 'in the last hours in Porto', Mendes held positive discussions with the club's football director Mateu Alemany.
The agreement is expected to run until June 2027, although it is unclear whether the €1bn (£840m) release clause that Barcelona are thought to have demanded will be included.
Fati has been in impressive form for Koeman's team since returning from a serious knee injury, scoring in two of his last three league appearances.