Reports from beIN Sport claim United missed out on the Arsenal contract rebel.
The Wales international will be out of contract at the end of the season and has been linked with a move away from Arsenal.
Ramsey was offered a new deal, but the offer from Arsenal has reportedly been taken off the table, so everything seems set for an exit for Ramsey.
United boss Jose Mourinho is a fan of the midfielder and could be tempted into making another move for him in the January transfer window.