The pair face stiff competition from Leicester City who its reported have already been in contact with Old Trafford about the prospect of a January deal.
Carrick himself is in no hurry to leave United but having played only in the Carabao Cup this season against Burton Albion, knows his future lies away from the Theatre of Dreams.
Steve Bruce, the former Manchester United defender, is keen to bring more experience to Villa Park as he seeks to win promotion to the Premier League.
Landing John Terry in the summer has seen Aston Villa climb to the fringes of the play-off places. Strengthening his midfield with Carrick’s knowledge and experience provides Bruce with more leadership on the pitch, something the Villans were sorely missing in last year’s run-in.
West Brom and Leicester both hope the prospect of remaining in the Premier League will persuade Carrick to sign with them rather than the project Bruce is putting together in the Championship.
Tony Pulis sees his side currently struggling in 15th place, a disappointing position after last season’s 10th place finish.