The 23-year-old right-back hasn't figured in Peter Taylor's plans this season, with his only appearance being in the LDV Trophy First Round in October.
But Chester boss Mark Wright is interested in securing the player's services.
He told the Daily Post: "Carl is a quality player, who has an excellent playing pedigree.
"We will have a look at him and he will be taking a look at us. It is too early to predict if either party will take the matter further.
"But the lad is certainly the type of player we are looking for."
The Liverpool-born former Everton trainee was signed on loan by Jan Molby from Barnsley back in August 2002. Peter Taylor then decided to snap up the player on a free transfer after taking over, but has since signed Marc Joseph, Richard Hinds and Alton Thelwell, leaving Regan's services unrequired at the KC Stadium.