The 23-year-old, who was named in the PFA League One team of the year, has been linked with a host of Championship outfits following his exploits this season.
However, Davis told the Crewe Chronicle: "He has another year on his contract and I think he'd be happy to see that through as captain and try to get us into the next league.
"Luke is quite chilled out. He is not desperate to go, he loves the club and he knows if he does well enough he will go anyway.
"I've spoken to the chairman and nothing has happened. That said, it was the same with Ashley Westwood this time last year and he left five games into the new season. If Luke was to leave I'd prefer it to be sorted earlier than that so I can get a replacement in."
Nick Powell and Ashley Westwood both left Crewe for the Premier League last summer.