The attacking midfielder aggravated an ankle injury during his national side's 2-1 victory over Scotland and could be left out for Tuesday night's fixture against Croatia
The 23-year-old lasted just 45 minutes against Scotland on Friday evening, having to be replaced at half-time after aggravating an existing ankle injury.
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"We only had Gareth for 45 minutes - and albeit a jaded Gareth Bale," the national boss told reporters of the Scotland match.
"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 okay. 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."