The Red Devils are being widely tipped to appoint Mourinho as their next permanent manager after United sacked Louis van Gaal on Monday night.
Mourinho hasn’t made a return to football management since he received his marching order in December following Chelsea’s disastrous start to the season.
Brazil international Willian was one of the only Blues players to emerge with any credit from the 2015/16 season after he impressed under both Mourinho and Guus Hiddink.
According to The Sun, the 53-year-old is keen to bring the £60m-rated midfielder to Old Trafford upon his appointment as United manager.
Willian scored five times and made six assists in 35 Premier League games for the west London side in an otherwise difficult campaign.
The 27-year-old move to Chelsea ahead of Liverpool in a £30m deal in 2013.
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