The striker has suffered an injury-plagued spell at Old Trafford, making just four appearances this season.
But the 32-year-old insists he is still able to continue playing for “two or three years”.
He told Sky Sports News: "I am only 32. I might look a bit older than that but obviously looking at the likes of Scholesy and Giggsy it doesn't half fill you with a lot of motivation and confidence that they are playing into their mid-to-late thirties and I still feel as if I am reasonably young.
"When I wake up my body feels good even though I have had a few injuries. I don't wake up with sore joints or anything like that.
"At 32 I definitely owe it to myself to still have two or three years and hopefully play a bit more for somebody else."
Owen managed 52 appearances for the Red Devils and scored 17 goals, but the presence of Wayne Rooney, Danny Welbeck and Dimitar Berbatov have all forced the former England international down the pecking order.
His last appearance in a United shirt came back in November of last year in the 2-0 Champions League win over Otelul Galati, when he was forced off with a thigh injury after just 10 minutes, and revealed on Wednesday that his contract was not being renewed.
"The manager informed me after our testimonial match on Tuesday that the club would not be offering me a new contract," the striker revealed on his Twitter account.
"I have loved every minute of the 3 years I have spent at such a fantastic club. I would like to thank the players, staff and fans for their support and wish them well for the future.
"I now plan to have a short holiday during which I will contemplate my next move."