However, Bruce denied any knowledge of the potential transfer and revealed that he had recently spoken to Red Devils boss Jose Mourinho over the goalkeeper's future.
Johnstone has played every minute of Villa's Championship campaign thus far, conceding just 24 times in 26 games.
"We haven't heard that at all," Bruce told BBC WM when quizzed about media speculation that Johnstone is about to move to West Brom.
"I spoke to Jose Mourinho two days ago and he never mentioned it.
"He not our player, of course, but we want him to stay. He's very, very happy here. Let's hope that's the end of it."
Bruce does not expect Villa to bring in new loan signings until the end of the January transfer window and signalled that he would blood young players in the club's FA Cup third round tie against League One side Peterborough United this weekend.
"We've got one or two things bubbling, but we have nothing lined up. With loans, I don't think anything will really happen until the end of January," the former Hull City manager said.
"It would be lovely now to be able to go and invest in one but obviously, with the situation we're in, we can't.
"And I've got young ones. The future of the club belongs to them. We've got some excellent young players.
"Callum O'Hare, Rushian Hepburn-Murphy, Andre Green, who will play on Saturday, and Keinan Davis, who is already in and around it. Throw them in. Why not?"
Villa are fifth in the Championship table, five points adrift of second-placed Derby County.