Arsenal wanted to take Bailly on loan until the end of the season with a view to a permanent deal in the summer.
But United do not want to lose the 24-year-old at this stage of the campaign and have no interest in doing anything that might assist a Premier League rival.
Arsenal have had an enquiry for defender Eric Bailly (right) rejected by Manchester United
Arsenal were interested in taking the 24-year-old defender on loan until the end of the season
Bailly has only started once in the seven games that Ole Gunnar Solskjaer has taken charge of
Arsenal need central defensive cover after losing Rob Holding to injury in a game at United before Christmas.
Coach Unai Emery has now lost Hector Bellerin too after the right back was ruled out for the season with a knee injury.
Emery knows he is limited to loan signings in this transfer window and thought he could exploit the uncertainty over Bailly's contract.
United and Arsenal are scrapping for a place in the top four of the Premier League this season and face each other in the FA Cup at the Emirates on Friday night.