United have had a bid accepted for the promising 17-year-old midfielder but the Welsh side have confirmed that another Premiership side have also been given permission to speak with the player.
"We can confirm that on Tuesday, June 3, Cardiff City have received formal bids from three top Premier League teams for Aaron Ramsey and that he has been given permission to speak to two of these teams," a Cardiif spokesperson has said.
"One of these teams is Manchester United, as has been reported, although at this stage we can confirm that no deal has been done and the player has not yet agreed terms.
"More details will be made available as they are released to us."