The Ghana international has been in the treatment room since August after withdrawing from a 2-1 Premier League defeat to Chelsea on 35 minutes, incidentally his first game for the Hammers since completing a three-year move from Swansea City.
He was initially ruled out of action for four months, but now looks set for an earlier comeback, with his recovery well ahead of schedule according to the club.
"Andre Ayew and Diafra Sakho are both progressing well and have been running on the pitch," West Ham head of Medical and Sports Science, Stijn Vandenbroucke, said in his latest player fitness update.
"We will introduce the ball to their rehab work soon, but it is too early to put an exact timeframe on their return to first-team action."
Ayew netted 12 goals in 34 league appearances as Swansea finished 12th in the English topflight last season.
He has also played for French sides Marseille, Lorient and Arles-Avignon.