Rooney asked to leave Old Trafford at the end of last season, and despite new Red Devils manager David Moyes insisting that he will stay with the Premier League champions, the England forward is still being tipped to leave United.
Chelsea are keen to add a striker to their squad and recently-reappointed boss Jose Mourinho has admitted his admiration for Rooney, of whom Hazard is also a big fan.
"Rooney would be a brilliant signing," he told reporters. "He's a great player who has the experience and he's still only young, at 27. He's got a few years left to play. But it's not up to me. It's not my decision."
It is understood that a fee of around £30m would tempt United into selling their fourth leading goalscorer of all time.