The former Hull City boss is in line to replace Roberto Di Matteo in the Villa Park hotseat, according to BBC Sport.
Bruce previously confirmed that he has held talks with the Championship club, but an official announcement is yet to be made.
Villa sacked Di Matteo after making a poor start to life in the second tier of English football, lying in 19th place in the league table after winning just one of their opening 11 games.
Bristol City boss Lee Johnson, Huddersfield Town’s David Wagner and Burnley manager Sean Dyche are among those previously linked with the Villa post.
Villa owner Dr Tony Xia has confirmed via Twitter that the club will name its new manager on Wednesday (October 12).