Morrison, who has rarely featured for the Hammers this season, had been said by Sky Sports to be on the verge of a move to Lazio, but Villa have apparently lodged some late interest.
The England youth international is available on a free transfer and Villa may have identified him as someone who could increase their attacking threat.
Paul Lambert's side have netted only 11 goals in 21 Premier League games so far this campaign and Morrison's skill and creativity is something which they may well feel could improve their side.
Morrison has fallen out of favour at the Boleyn Ground, with his attitude being blamed as the reason for his exclusion.
The 21-year-old has built up a bad-boy reputation during his time in the professional game so far, but his talent is unquestionable.
Morrison is a capable dribbler, who also possesses masses of technically ability and he can be a match-winner at any level on his day.
The hope will be that a move to Villa, where he will surely be made one of their main attacking outlets, could focus him and allow him to fulfil his very obvious potential.