Owen's current Old Trafford deal expires at the end of the season, and with the emergence of young forwards like Javier Hernandez and Federico Macheda, the chances of him being offered a new contract could be slim.
And rather than join a 'lesser' club, Owen suggests he may call it a day.
Owen, who will turn 31 in December, is quoted in The Sun as saying: "I would honestly love to stay, but you will have to ask the manager about the long term. I could score at this level for many years and would love it to be at a top club like United.
"Whether I would want to be dropping down to a poorer Premier League team, I don't know. Yes, I could score goals but I would probably get less opportunities and less enjoyment.
"I just don't feel my game is suited to a team that is really struggling. I won't drop down leagues.
"I have played in big teams before and played every game and I have played in a struggling team. I know which I prefer. When you play here, you play with quality."
And Owen already seems to be looking towards his post-playing career: "I'm on my second stage of coaching badges and management is a real possibility," he said.
"Horse racing will always be a big part of my life but, if there's a job going forward, it will be in football."
Owen has started just six league games since arriving at Old Trafford last summer, and while his scoring record is good, he is likely to slip further down the United pecking order.
The former Liverpool, Real Madrid and Newcastle forward is currently sidelined with a hamstring injury, but he doesn't believe his fitness record has hampered his United career.
"I was fit for most of last season but got the injury in the Carling Cup final," he added.
"I'd like to play as much this season but this injury has been a kick in the teeth."