The 23-year-old, who scored six times at the 2012 London Olympics, has been courted by several English clubs throughout the past 18 months.
Tottenham Hotspur have been linked most heavily with his signature, but were believed to have had an insufficient offer rebuffed for him this summer.
However, Internacional president Giovanni Luigi has stressed that their star asset will not leave for less than his asking price.
He told Zero Hora: "We aren't talking about a small team. We are talking about Internacional. [Manchester United] have to talk with Internacional, not with the player.
"If Manchester United came here today, I would ask them to pay his buyout fee. They have to know that Internacional are a big club.
"Now, Leandro Damiao only leaves if the buyout fee is paid."
Leandro has been capped 10 times by Brazil, scoring twice since debuting in 2011.