Keane had spoken to Birmingham about a £7m move from Tottenham Hotspur but talks stalled and Birmingham who play the Sky Blues in the Fourth Round of the FA Cup have switch their interest elsewhere.
The Republic Of Ireland international is being cited as not wanting to move house and a London club would suit him but he may have to take a drop in his reported £65k a week wage.
West Ham are being reported as being willing to pay something around his current wages but Fulham would, according to media reports, want him to take a 30% pay cut.