The Belgium international midfielder joined the Red Devils from Everton on transfer deadline day for a reported fee of £27.5m.
"Keane was an aggressive player who could win every ball. Maybe I can do this as well," BBC Sport quotes him as saying. "I can win the ball. I can clear the ball. I can play clean."
Keane played for United from 1993 to 2005 and helped the club win the Premier League seven times, the FA Cup on four occasions and the Champions League once.