The 23-year-old Bale lasted just 45 minutes in Wales' come-from-behind, 2-1 victory over Scotland on Friday, having to be replaced at halftime after aggravating an existing ankle injury.
"We only had Gareth for 45 minutes - and albeit a jaded Gareth Bale," Coleman told reporters. "He's been ill and had a knock on his ankle but he wanted to play. He said he felt fine so that's why we started him. He had another knock after 30-35 minutes on the same ankle, so we had to bring him off.
"I don't know if he will be OK. I'm not sitting on the fence, but the next 24 hours will be crucial. All we can do is wrap him up in cotton wool. If he is not ready, then we can't risk him.
"We won't, because we have to be fair to Tottenham. They never stand in his way, and he always comes along. Gareth likes to come, but we have to look after him."
A win for Wales on Tuesday would put Coleman's side four points behind Croatia, which currently occupies the second spot in Group A.