This is according to the Independent, who understand the Argentina international is prepared to run down his contract in order to leave the Parc des Princes as a free agent this summer.
Lavezzi is free to sign a pre-contract agreement this month but a late bid is likely to be accepted by PSG, who are aiming to recoup some of the €30 million they paid Napoli in 2012.
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The 30-year-old has played a bit-part role at PSG this season - he’s only completed the full 90 minutes in one Ligue 1 match - and would prefer to return to Italy.
Juventus and Inter Milan are also keen on the Argentine, but United and Chelsea can offer more money - both in terms of a transfer fee and wages.
Both Chelsea and United could do with Lavezzi
Chelsea, according to the report, are the club most keen to secure a deal for Lavezzi due to the poor form of Eden Hazard, who scored his first goal of the season against MK Dons on Sunday, and Pedro.
United, meanwhile, could do with bolstering their forward line to ease the goalscoring burden on Wayne Rooney and Anthony Martial.
But Lavezzi is likely to stay with PSG
However, it’s difficult to imagine Lavezzi ending up at either Stamford Bridge or Old Trafford before the transfer deadline passes.
Time is rapidly running out and Lavezzi may be keen to stick with PSG until the summer - so he can pick up his Ligue 1 winners’ medal and perhaps even a Champions League winners’ medal.
Do Manchester United or Chelsea need Ezequiel Lavezzi? Have your say by leaving a comment below.