The 26-year-old, who has been convinced by David Moyes that he has a role at Old Trafford, has also been targeted by Paris Saint-Germain and Zenit
Goal exclusively revealed earlier in July that David Moyes has convinced the Portugal international to remain at Old Trafford this summer.
The 26-year-old, who made just seven starts in the Premier League last season, has been targeted by Ligue 1 duo Paris Saint-Germain and Monaco, as well as Russian side Zenit St Petersburg.
"No, Nani is just rumours. Our market is closed," Ranieri told reporters.
Monaco secured their first win of their pre-season campaign on Saturday afternoon after Layvin Kurzawa, Radamel Falcao and Marcel Tisserand scored in a 3-0 victory over Leicester City.