The England international is expected to be loaned out before the end of January after making just three appearances in all competitions this season.
According to the Evening Standard, West Ham are the favourites to conclude a deal for the 28-year-old as they bid to remain in contention for the top six.
Like West Ham, Villa are competing for European qualification, and Lingard would be regarded as a valuable addition given his big-match experience at Old Trafford.
Meanwhile, the playmaker would likely become a first-team regular at relegation-threatened Sheffield United if he opts to move to Bramall Lane. body check tags ::