In an exclusive interview with Goal, Rebic revealed that he was glad to hear of reported interest from Jose Mourinho, and admitted that there had been "concrete offers" to sign him.
The transfer window for Premier League clubs ends at 17.00 BST on Thursday, with Mourinho have frequently expressed his frustrations at a failure to bring in new signings.
Diego Dalot, Fred and Lee Grant are the only United arrivals thus far, with the Red Devils' chase for a centre-back seeing them agree a deal for Toby Alderweireld although with the caveat that Tottenham find a replacement.
It would appear that Bayern will not be direct rivals in any move for 24-year-old Rebic, however, with head coach Niko Kovac having insisted he is not currently a player they're looking to buy.
He told Sport Bild: "There is nothing between FC Bayern and Ante Rebic. He is a strong personality and a great player but [a transfer] makes no sense. It doesn't make sense today, and it won't tomorrow."
Mourinho's side have also been linked with another Bayern player in Jerome Boateng, but the latest reports from Germany suggest that the player has informed the Red Devils that he is not interested in a move.
United get their Premier League campaign underway on Friday evening as they face Leicester City at Old Trafford.