The pair share an agent, Federico Pastorello, and hope a deal can be reached although United are unprepared to lose Lukaku cheaply and would want to recoup their £80 million investment in order to sanction a sale.
The United striker, 26, scored only 12 times in the Premier League last season but took his worldwide record to 48 goals after scoring twice in Belgium's 3-0 win over Scotland, which kept them top of Group I in qualifying.
It is obvious that his reputation has taken a hit in the Premier League and his confidence, at club level, is pretty much at an all-time low.
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He added: "With the transfer of [Cristiano] Ronaldo, I think the Italian league is now coming back".
Conte was appointed as Inter's new head coach last month, and reports suggest the Italian side could launch a move to bring Lukaku to Serie A as he bids to strengthen his squad this summer.
Lukaku said he has made a decision about his future, but he may not have the final say should something happen.
Manchester United are set for a big summer, with the club expecting several incoming and outgoings.
The Red Devils have not won a major trophy since their Europa League triumph in 2017 under Jose Mourinho. However, he lost his place to Marcus Rashford when Ole Gunnar Solskjaer came in.