The 50-year-old was sacked after a poor run of six successive defeats in the Premier League that has left them in 17th place - only two points from the bottom three.
Smith - an Aston Villa fan himself - joined the club in October 2018, with former Chelsea and Villa defender John Terry also joining as his assistant head coach.
Despite the club sitting 14th in the Championship at the time of their arrival, the pair helped Villa to win promotion to the top tier in the same reason and Terry remained alongside Smith until his departure in the summer.
Following Smith’s sacking, ex-Aston Villa and England forward Gabriel Agbonlahor has encouraged Terry to return to Villa Park.
Speaking to talkSPORT, Agbonlahor said: I actually think he would come back.
“I think he wanted some time with his family after such a long career, straight into coaching, being in Birmingham alot, but I feel like now if Aston Villa wanted him back as a coach i think he would come back.
“JT get yourself back in there now, holiday's over!"
The former England captain’s only coaching experience is his three years with the West Midlands club, but since his departure in July he has been linked with numerous clubs including Newcastle United and, most recently, Norwich City.
Terry is yet to entertain any rumours of him returning to work, however a move back to Villa Park may be of more interest to him compared to other clubs previously mentioned.
It has only been a matter of hours since Smith was sacked, but there has already been a host of names linked with the managerial vacancy with Terry’s ex-England teammates Steven Gerrard and Frank Lampard both favourites.