Last season the 20-year-old made two appearances for the Red Devils in the Capital One Cup and went on to end the campaign with Leicester City on a loan deal.
Having now returned to Old Trafford, Keane is hoping that he will be given the chance to impress incoming manager David Moyes during the summer trip.
"I'd love to go there. It'll be a great pre-season tour. I think if I can get on the tour and do really well, it would stand me in good stead for next season. I'm looking forward to it and hoping I can get on the trip," the England youth international told Inside United.
Keane signed a professional contract with United in January 2011.