The Wales international is a reported target for Remi Garde’s men.
The Wales international was signed by former Reds boss Brendan Rodgers but has failed to consistently win over the Anfield faithful since his move from Swansea.
With Jurgen Klopp’s appointment after the Northern Irishman’s dismissal, Allen’s future is a point of contention as he is struggling for regular first-team football.
The 25-year-old has only made three substitute appearances in the Premier League this season that has accounted for a mere 20 minutes of action.
The likes of Jordan Henderson, James Milner, Lucas Leiva and Emre Can are all ahead of Allen in Klopp’s preferences, leaving him as a fringe figure.
Villa meanwhile find themselves bottom of the Premier League table and look destined for a relegation battle this season.
Remi Garde has replaced Tim Sherwood in the Villa Park hot seat and will naturally be looking to bring a few new faces to the club in January.
Calciomercato claim that Allen is in the Birmingham-based club’s sights and that a deal could well be done in the new year.