The 29-year-old has not started for Doncaster this season, but Davis has suggested that the experienced striker would play a key role in his side.
"I'd like to get a striker in. If we are going to spend some money, that's the right area," Davis told the Crewe Chronicle.
"He doesn't have to be great at linking the play - just be on the end of things. Paynter has a great record, he's experienced and scored two for Doncaster against us last year.
"He wouldn't chase down the channels but we won't need him to, we'd need him to get on the end of the crosses and he has the expertise to tuck them away. Our forwards haven't been able to do it on a regular basis and it is a concern."
Paynter's seven appearances for Doncaster this season have all been from the bench.