Bruce was recently appointed as Villa manager following the sacking of Roberto Di Matteo and the former Hull City boss, who was in the running for the England job at one stage, started his rein off with a 1-1 draw against Wolverhampton Wanderers on Saturday.
The Birmingham-based outfit did add notable attacking options to their squad in the recent summer transfer window, bringing in Ross McCormack and Jonathan Kodjia for a combined £27million.
However, the new manager is still keen on strengthening this department and, according to reports, Rhodes has been outlined as the number one target in January.
The Scotland international has made just one Premier league start this season and the lack of playing time is becoming a real frustration for the striker.
Bruce is hoping to tie up a loan deal when the next transfer window opens with Boro receiving a bonus payment if Villa manage to get promoted from the Championship.