Nick Powell and Ashley Westwood earned moves to Manchester United and Aston Villa respectively following their key roles in Alex's 2011/12 promotion from League Two.
Luke Murphy took the captain's armband upon Westwood's departure and went on to produce an inspired campaign this time around, capped by a superb opening goal in the Railwaymen's 2-0 Wembley triumph over Southend in the Johnstone's Paint Trophy final.
Such displays have fueled speculation the 23-year-old will move on from Gresty Road but, according to Davis, no enquiries are forthcoming at this stage.
"We've had no enquiries but it is early yet," he told Crewe's official website. "I'm sure most managers are making calls and devising lists. They just won't have one or two on it but five or six.
"I'd expect things to happen later in June or early July. We are like any other club. Our recruitment is on-going - we are talking to agents, we've invited a couple down to speak to.
"It is still quiet but will get busier as we approach the pre-season games."