Adomah was linked with a move from Villa to Leeds in the summer.
The 30-year-old shone for Villa last season during the Midlands club's push for promotion, proving to be a crucial part of their campaign as they reached the play-off final.
Last season, Adomah found the back of the net 15 times as well as creating another seven assists during 44 outings, meaning he had a hand in a goal every two games.
The Birmingham Mail claimed in the summer that Leeds were interested in 18-time Ghana international Adomah, as well as former club Middlesbrough and West Brom. But Adomah is set to stay at Villa, according to Bruce.
“Albert has been great for me since I have been here,” Bruce said. “I have picked him more than most since I have been here. He plays almost every week. Now we have a bit of competition, which can only be good.
“The competition nearly got us there last year. Albert is a valued member of the squad. You can’t help but like him. He is a great pro, a great lad who had a great season for me last year. I hope he can get off and running again.”
Adomah's position in the side is under threat at the moment, with Villa completing deals to sign Yannick Bolasie on loan from Everton while Anwar El Ghazi has joined on a temporary basis from Lille.
It remains to be seen if the former Bristol City speed machine will be given the game time he requires, with clubs likely to become interested in January if he is used as back-up between then and now.