Owen has only had one start for United in the Premier League this season and is currently out injured.
"I don't think I'm going to do a Giggsy and play into my late 30s but I'll definitely do two, three, four years it just depends," the 31-year-old told Soccer Saturday.
"I would love to (stay at Manchester United). It might not be realistic because Man United are one of the world's best teams and there's always youngsters coming through and top players there, so I would love to but I'd have to be playing a little bit, a bit more.
"But I've spoken to the manager on these topics a few times so we'll sit down again at the end of the season and discuss where we've gone, but I've loved every minute of it.
"My decision to go to Manchester United was one at the start of 'Okay I'm not going to play every week but I'll be keeping my level and standard high, training with the best players. When I do play fantastic team, stadium, fans playing under an unbelievable manager'.
"There was so much to look forward to, and I think people would be foolish if they think that I'd move to a team lower in the league when Man United were calling.
"As soon as the call, the first thing I thought was I'm going to see what the manager's like in his team talks - that was one of the main things that was exciting about joining Manchester United."