Without the flanker, the Blues are ninth in the RaboDirect PRO12 and face Bath this weekend in the Anglo-Welsh Cup.
And Davies admits there is a chance Warburton could feature either against Bath or at home to Harlequins the following weekend.
He told WalesOnline: "He has made great progression that's for sure, and he's had a good week (last week).
"I have spoken to Warren (Gatland). We just want to make sure we do the best for Sam. He is in a position where we have to make sure he is 100 per cent.
"That might be next week, the week after or whatever the case might be ... but he is a lot closer than he has been.
"It's days, maybe a week or so, when previously it has been months. Who knows? He could possibly play in one of our next two games, we'll see."
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