The Premier League side are supposedly keen to add some more firepower to their squad at the end of the season and reports from Italy suggest they have earmarked Icardi as the ideal addition to strengthen their attack.
Nevertheless, the 22-year-old has stressed that he is happy with life at Inter and would reject an offer from United.
"I am feeling very well in Milan. I want to stay here for a long time," Icardi told Corriere dello Sport.
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"I received a number of offers when we were discussing my contract renewal with the club, but I had already taken my decision.
"I would also turn down Manchester United. Inter are working on a great project and I want to play my part in it.
"People say I am worth €40million, but it is up to me to prove I am worth that much money.
"I am committed to this team and happy to be part of it."
Icardi, who has a contract with Inter until June 2019, has netted 10 goals in 21 Serie A appearances this campaign.