British media reported that United have offered 36 million pounds ($55.49 million) for the 19-year-old, who scored nine goals in 35 Ligue 1 appearances last season.
The 24-year-old Borini spent a successful year on loan at Sunderland in the 2013-14 season, scoring 10 goals to help the northeast team stay in the Premier League.
It was unclear whether the clubs would appeal to league authorities or FIFA in an attempt to push the deal through.
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