Lacazette could, however, end up remaining in his homeland if a summer transfer is made.
Lyon president Jean-Michel Aulas says he would prefer to deal with a domestic rival rather than sanction a big-money sale to England.
He told France Football: "I know Nasser suggested to Noel Le Graet [president of the French Football Federation] that he is not investing that much in French players because he thought other presidents of French clubs looked badly upon it.
"I want him to know that if he makes an offer for Alexandre at least equal to that of the other clubs bidding for him, then Alex can go to Paris without problem.
"I am a businessman and a modern club president. Transfer money must be reinvested into French football, as I always did when we were at the peak of our powers.
"When transfer money is shared abroad, it strengthens our competitors instead."
Lacazette has enjoyed a goal-laden spell with hometown club Lyon.
He burst into life during the 2013-14 campaign and has now netted 129 times in 275 appearances for the club.
That haul includes a personal best tally of 37 from the 2016-17 season, with those efforts returning him to the Ligue 1 Team of the Season.
Were he to move to PSG, Lacazette would team up with another potent frontman in the form of Uruguay international Edinson Cavani.