Smith suffered a very bad leg and ankle injury during an FA Cup match at Liverpool earlier this year, and although he is now fit again, he has struggled to get back into the Manchester United team this season.
Sir Alex Ferguson revealed last month that he is happy to see the player leave in a loan move.
Leeds and Cardiff were rumoured to be interested in taking him into the Championship but he prefered to stay at Old Trafford.
However, with Henrik Larsson joining the Reds in January, Smith knows his chances of regular first team action will suffer and rumours suggest he is ready to accept a six-month loan spell at Villa Park.