The Railwaymen prop up the table, having earned just nine points from 16 games this season, with current boss Steve Holland's future at Gresty Road still under discussion.
Holland had defiantly said he would not quit the club, but it has been taken out of his hands.
Holland took charge at Crewe in the summer of 2007, but has struggled to win over the club's fans, as the team struggle to avoid relegation to League Two.