Keane impressed during a temporary spell at Ewood Park at the end of the last campaign, but while he has admitted that he is fan of the 21-year-old, Bowyer expects the centre-back to feature at Old Trafford in the near future.
The 42-year-old told BBC Radio Lancashire: "The lad is Premier League for me - he's got that quality. He's a Manchester United player and they've got a new manager.
"We continue to monitor it but I fully expect Michael to be in and around Manchester United's first team, especially over pre-season, so that they can have a good look at him."
Keane scored three times in 13 appearances for Rovers during the final two months of the season.