The Belgian centre-back has not featured since sustaining a knee injury against Crystal Palace in November, but has now returned to training.
Elsewhere, City manager Pep Guardiola suggested he would resist the temptation to rotate his side given the difficult challenge West Ham are likely to present.
The boss said: “We play West Ham away… they are a Premier League team, we are away, it’s tough. I want to continue in this competition.”
He added on Kompany: “He has started training now but he’s not ready to play tomorrow.”
Guardiola reiterated how happy he was with City’s battling performance against Burnley on Bank Holiday Monday, when the Blues secured three points despite having Fernandinho sent off in the first half.
“I was so happy for our victory, it was important,” he reflected.
“If we had dropped points against Burnley it would have made life difficult.
“Sometimes I’m so demanding and the players showed how special they are.
“Burnley are not an easy team, they are doing exceptionally, we’ve beaten them away and home - 10 v 11 and that’s why I’m so happy.”
Guardiola spoke about his anticipation of experiencing the magic of the FA Cup for the first time.
He declared: “In the Bundesliga, the cup tradition is special. What I hear here is that the Cup is special because the low teams can beat the big teams - that’s why it’s fascinating.
“I’m looking forward to it. We were unlucky in the draw.”
