The 30-year-old Argentine international may well see his standing at the Parc des Princes side restricted by the arrival of fellow countryman Angel Di Maria from Man United.
Tottenham have previously been linked with an interest in Lavezzi, who has had an up and down time of it since leaving Napoli to join the Ligue 1 side three years ago.
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Louis van Gaal is keen to strengthen his attack and had been hoping to sign Pedro but a move for the Spaniard has been delayed due to Brazilian Neymar suffering an attack of the mumps that will see the Barcelona man sidelined for the opening weeks of the campaign.
Lavezzi is capable of playing in a central of wide-attacking role and has scored 32 goals in 136 appearances for PSG.