Davis had hoped to sign Leigh, who made 42 appearances while on loan last season, following his release by Manchester City. But the 19-year-old's wage demands have so far proved well out of Crewe's reach.
"We can't afford what Man City paid Greg. We have to be realistic with that," Davis added. "What we can do is give him the opportunity to play. I've stressed that to Greg's agent, but I've heard nothing back."