Manchester United boss Louis van Gaal has said that Darren Fletcher's proposed move to West Ham is off.
Hull boss Steve Bruce says his side's 3-0 defeat to Newcastle may have jeopardised his chances of strengthening his squad.
Keane spent time on loan at Ewood Park last season but has returned to parent club Manchester United this summer to try and impress new boss Van Gaal.
Van Gaal has made it clear that he will take a look at everyone in his squad over the next few weeks before deciding on whether he needs new signings, and Keane has travelled out to the USA with a 25-man United squad for their pre-season tour.
Bowyer has already snapped up Alex Baptiste on loan from Bolton Wanderers, but he says he would still be keen to take back 21-year-old defender Keane if the opportunity arose.
“I’ve said all along that Mr Van Gaal will have a look at him,” said Bowyer in the Lancashire Telegraph, speaking before this week’s warm-weather training camp in Portugal.
“If Michael’s situation was to change then hopefully we’d be in a position to put ourselves forward.
“But we’re talking ifs, buts and maybes at the moment as he’s a Manchester United player.”