The forward is considering leaving Old Trafford after becoming disillusioned at the club.
Rashford was left out of the Manchester derby by coach Ruben Amorim, who has been unhappy with the forward’s application and attitude.
Speaking on the Stick To Football podcast, Keane said: “I don’t actually mind what he said, although it’s a bit long, but it’s spot on.
“Sometimes a deal just works for everybody - it’s been going on for a year or two now. There’s obviously a bit of talent there and he’s been at the club since he was a kid.
“A change would probably do him a world of good, for him and his team and family to go abroad.
“My only warning for players like that – he (Marcus Rashford) has all those traits as a footballer. If you lose that hunger, it’s hard to get it back.
“We know that for great players, it’s nothing to do with money - it’s about the next challenge and your pride.”