Mancini has reportedly told confidants he's in the frame to replace Ruben Amorim as United manager.
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The Italian is available after leaving the Saudi Arabia post last season.
Mancini is said to have links to United co-owner Sir Jim Ratcliffe.
Like the 72-year-old, Mancini also has a base in the south of France while he is believed to have crossed paths with him at various social functions.
The Sun says the former Inter Milan and Italy coach has told friends should Amorim be axed that he would be a contender for the post.