Finnan picked up a thigh injury in the Champions League final and had to be subsituted at half time. He is now facing a race against time to be fit for the Israel game this weekend.
"I doubt if he will be back for Saturday but he has some chance," said Ireland boss Brian Kerr.
"I'll just wait for the reports. He's still a fair bit to do - running, kicking and jumping - but the game is on Saturday so there is time."
