Clarke has guided Scotland to the World Cup this summer, with his deal expiring at the end of the tournament.
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Celtic great Dalglish has called on the SFA to hand Clarke a new deal: "He'd be a hard act to follow if he was to go somewhere. It's all supposition, isn't it? Just let the World Cup happen.
"And then, afterwards, if he's got a decision to make, he's got a decision to make. I don't think he'll have a problem renewing his contract here. I think it would be rather silly not to give him a new contract.
"Stevie will do what Stevie wants to do. Everybody's contract runs out sometime, doesn't it? But I tell you, it won't be on results if he doesn't stay."