New Inter head coach Conte is reportedly keen to sign Lukaku, having missed out on the Belgium striker during his time in charge of Chelsea after he opted to join Premier League rivals United for £75 million ($95m) in 2017.
"I have a contract with Man United," said Lukaku, who scored twice against Scotland. "I'll speak with my club and my agent Federico Pastorello to make the best decision.
"I am going to enjoy my holidays with my family now. I know what I'll do but won't say it.
"We'll see. If I expect a busy summer? Yes."
Lukaku – contracted to the Red Devils until 2022 with the option of a further year – scored 12 Premier League goals as United finish sixth in 2018-19, missing out on Champions League qualification.
He scored 15 goals across all competitions for United in total, who lost to Barcelona in the Champions League quarter-finals.
The imposing centre-forward was unable to build on his promising debut campaign at Old Trafford, during which he managed to hit 26 goals under Jose Mourinho's stewardship.
Lukaku enjoyed a brief resurgence after Ole Gunnar Solskjaer's appointment as interim United boss back in December, most notably scoring twice in a stunning Champions League win over Paris Saint Germain.
However, his form dipped dramatically between March and May, with many fans and experts calling his fitness levels and technical ability into question.