The 30-year-old winger had an impressive season under Louis van Gaal in 2014/15 and was expected to be rewarded with an extension this summer.
Young's current deal expires at the end of next season but he says that no fresh proposal has been forthcoming as he continues to prepare for the upcoming campaign with the Red Devils in the USA.
"I'm at one of the biggest clubs in the world so I want to stay here as long as possible," he said.
"That's exactly what I want to do. I think a lot of people thought I had it done [a new deal] but I haven't. It's in the club's hands now so I will have to see how it goes."
Despite the fact his future remains uncertain, Young insists he is feeling calm and relaxed as he looks to but his best foot forward and further impress van Gaal during summer training and matches.
"Of course. I want to go out and play and at the moment I am on tour so I am trying to enjoy myself," he added.
"I hope we can sort things out. There have been preliminary talks so I am just looking to go out on the pitch and leave my agent to take care of that."
Regarding a new contract being finalised soon, Young said: "You will have to ask the club that."