TalkSPORT reckon the Ligue 1 champions are keen to snap up the talented forward.
However, reports last week suggested the influential star was set set to sign a new deal with Fiorentina.
“Federico Bernardeschi has been linked with Man United and Chelsea”
The club are sitting in mid table – but losing their influential forward could derail their season.
Italian news outlet CalacioMercato suggested owner Andrea Della Valle is preparing to offer Bernardeschi a bumper new deal in a bid to keep his prized asset.
That would see the winger receive a significant increase on his £850,000-a-year salary.
Chelsea and United are both expected to bolster their squads in January.
The Blues are flying high in the league and have now won 12 games on the bounce.
The Red Devils are improving after a slow start to life with Jose Mourinho.
But the Portuguese looks set to shuffle his squad when the transfer window re-opens as he eyes a top four finish.