Dee also said he has offered Davis an extension to his current contract, which has three years remaining. Dee would not divulge the terms of the contract proposal.
"We're doing everything we can to keep him," Dee told the Palm Beach Post for Sunday's editions. "The ball is in his court. We'll see what he wants to do."
Alabama athletic director Mal Moore called Dee late last week, Dee said, asking to speak with Davis about the Crimson Tide's coaching vacancy.
Mike DuBose was told last month that he would not be brought back for a fifth season. The Tide finished 3-8, their worst record since 1957, after being ranked as high as No. 3 in preseason polls.
Dee said he did not think Alabama had contacted Davis yet, but he expected that to happen this week. Davis has repeatedly denied having had any contact with Alabama officials.
"We're hoping he says no," Dee said.
According to Miami officials, Davis will not be "on the grounds" of the university on Sunday and Monday. They refused to say where Davis would be.
Davis, 49, is in his fourth year of a seven-year deal that pays him about $900,000 annually.
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