Milan are aware that United boss Louis van Gaal wants to see the Portugal international sold before the start of the season and have been in touch.
The Rossoneri believe they can do business for around €10 million, but Nani's personal terms will prove difficult to cover.
The midfielder is currently on around €3.5 million-a-year.
New Milan coach Pippo Inzaghi, meanwhile, has made a new winger signing a priority.
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