Varane, 28, was unveiled to the Old Trafford crowd on Saturday prior to their victory over Leeds.
He has signed a four-year deal with the Red Devils and joins for a fee of around £42million.
The Manchester Evening News says Jones has refused to depart with No.4 despite not playing for United since January 2020.
Jones is currently working his way back to full fitness at United, with Ole Gunnar Solskjaer declaring his commitment to the former England defender. He has two years remaining on his contract.
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