"We are as bemused as anyone can be, we can't quite understand why he would want to leave," Ferguson told a news conference.
The manager said Rooney would not play in Wednesday's Champions League match against Bursaspor because of an ankle injury.
A United press officer said that Rooney was taken off on a stretcher at the end of training on Tuesday.
Ferguson said a scan showed minor damage, which required treatment on his ankle.
"I feel that we still have to keep the door open for him — especially as he's such a good player," said Ferguson.
"We've done nothing but help him since he's been at this club. We're as bemused as anyone can be and can't understand why he would want to leave." Rooney joined the club in 2004 as an 18-year-old for a 25.6 million pounds ($40.40 million) fee, a world record for a player aged under 20.
He helped them to Premier League titles in 2007, 2008 and 2009 and the Champions League in 2008.
