Manager Steven Gerrard has made it clear he wants to strengthen his midfield options.
And Gallagher could prove an intriguing option with the 22-year-old eager to play regular football next season in a bid to force his way into England’s World Cup squad.
The midfielder impressed on loan at Crystal Palace last season.
The year before, he enjoyed a successful loan at Albion. And while his long-term goal is to establish himself at Chelsea, boss Thomas Tuchel is unable to give him assurances over his playing time.
The London side are also believed to be interested in signing Sporting Lisbon midfielder Matheus Nunes.
Villa will face strong competition, though, if they do move for Gallagher with Crystal Palace interested in re-signing him and Everton also thought to be keen.