PSG have been holding talks with Lyon in an attempt to agree a deal for Barcola, but there has been no breakthrough yet.
Lyon were given an offer of €30m plus bonuses for Barcola, which was styled as a final offer from PSG, but was one Les Gones have rejected.
With no agreement in place, the door may be open for other clubs and, according to French radio station RMC, Manchester City and an unnamed Premier League side are keen.
They are admirers of the 20-year-old Frenchman and could make a move to try to snatch him away from PSG.
PSG though have put serious legwork into the deal and coach Luis Enrique has already spoken with Barcola about the move.
It has been suggested that €50m may be needed to sign the Lyon man and talks are continuing between the two clubs.
Attacker Barcola made 26 appearances in Ligue 1 for Lyon last season, scoring five times and providing nine assists.
Lyon are determined he will not leave for less than they believe him to be worth.
