Davis has not been approached by Alex, who are looking for a new number two after deciding to replace the long-serving Neil Baker.
Davis, who played over 150 games for the Railwamen having been signed by Dario Gradi from Stoke in 1983, told the Sentinel: "I have spoken to my chairman and he knows I am ambitious and that I want to move on at some point.
"I want to test myself at a higher level. I am looking for the opportunity to further my career, be that as manager, assistant or first-team coach. I have made that clear, whether that be at Crewe or somewhere else
"I have read the papers and seen the rumours but I have not had an approach from Crewe, so they just rumours."