The Italy international winger joined Torino from Fiorentina in the summer of 2012 and has been impressive in the Serie A this season.
The Daily Star reports that United have been keeping tabs on Cerci for a number of months and are considering making a move for the winger in January.
But United now face competition from Arsenal as manager Arsene Wenger is ready to make a January move for the winger.
Serie A champions Juventus are also reportedly interested in the winger, valued at £16million by Torino.
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