The 31-year-old picked up the first Premier League title medial of his career on Sunday.
Owen’s current contract with United is set to expire this summer.
“I want to stay because Manchester United is a fantastic club,” he said.
“I have to find out in the coming week or two and I will be speaking to the manager.
“This is an important week so there is no point discussing my future with him now, but we will have a chat after the season is over.”
“You can drop your level and play more regularly in a team that is not of as high a standard as Manchester United,” added Owen.
“But your level stays high when you are training with top players and you enjoy your football much more when you are playing in a good team.
“It depends which side of the coin you look at.
“I have certainly enjoyed my time here even though I haven’t played as much this year and I have still felt part of it.
“I have played in 11 Premier League games and qualified for a medal and loved every minute of it.”
