The 23-year-old has made one appearance for the Premier League side this season following a string of injury problems.
Coyle is now keen to bring Albrighton the DW Stadium, subject to Villa boss Paul Lambert being happy with the move.
"He is a very good player, he is a player I tried to sign at Bolton a few years ago but he's an Aston Villa player and until Paul decides otherwise then that's how it is," the Scot is quoted as saying by BBC Sport.
"But we are always in the market for good players and he is certainly one of those."
Albrighton signed his first professional contract with Villa in 2009 after graduating from the club's youth academy.