Murphy capped a superb personal season by earning a place in the PFA League One team of the year, an accolade that comes on the heels of his excellent goal in Alex's 2-0 Johnstone's Paint Trophy triumph against Southend at Wembley.
Such performances have made the 23-year-old a sought-after prospect and he is tipped to follow former team-mates Nick Powell and Ashley Westwood in making a high-profile move.
Powell and Westwood starred in the Railwaymen's League Two promotion campaign last term before earning respective summer switches to Aston Villa and Manchester United.
Davis accepts Murphy could well go the same way but does not want any deal to run close to the August transfer deadline, as was the case with Westwood eight months ago.
"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," he told the Crewe Chronicle.
"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."