The Belgian has subsequently labelled new Inter boss Antonio Conte "the best coach in the world" as speculation about his future continues to mount.
Lukaku scored a brace in Belgium's Euro 2020 qualifying victory over Scotland on Tuesday night, helping his side to a 3-0 win.
"He knows what I think of him, I don't like discussing my relationships with coaches in public".
United are prepared to listen to offers for the Belgium worldwide but want to recoup the transfer fee they paid Everton in the summer of 2017.
"I've already taken a decision about the future, but I can't reveal it because I have a contract with Manchester United and because I respect the club", he added.
"I've had a hard season at club level", he added. I've already taken my decision.
The United striker, 26, scored only 12 times in the Premier League last season but took his global record to 48 goals after scoring twice in Belgium's 3-0 win over Scotland, which kept them top of Group I in qualifying. I think Serie A will be really exciting next year and I'm really happy for Italian football.
"It's up to the club", Lukaku said.
"But that is a phase in my career and it will help me for the next step".
"I'll speak with my club and my agent Federico Pastorello to make the best decision. I would have loved to been in amongst it especially pre-match when this was going on".