The 24-year-old signed at Old Trafford this summer for £75m from Everton.
Jose Mourinho reunited with the hitman who is set to lead the line for United for years to come.
Lukaku penned a five-year contract this summer with the option for a further season.
That could see him stay at United until 2023, and he intends to stay long term.
The Belgium star was asked about a potential buy-out clause in his deal which could attract other clubs down the line.
But Lukaku told Belgian newspaper DH: “I don’t have one, I’m very happy.
“I hope I stay there for a very long time.”
Lukaku refused to discuss how big an offer it would take for United to sell him.
He added: “I’m not going to leave. I’m happy over there.
“Manchester United is a big club."
Chelsea boss Antonio Conte was vying for his signature as well this summer, but the Blues were pipped to the striker by United.
Lukaku has made an immediate impact at Manchester United, scoring three goals in three Premier League games.
Once he returns from international duty, he is set to start at Stoke next Saturday.
