The French side are looking to bolster their midfield options having cancelled a move to sign Swiss star Hakan Yakin.
PSG have lined-up Van Bronckhorst and Chelsea ace Boudewijn Zenden as possible alternatives to Yakin for the left-sided role in their side and watched the duo in action in Wednesday's draw between Holland and Belgium
Van Bronckhorst has failed to establish himself at Arsenal since his arrival from Rangers in June 2001 due to a series of injuries.
PSV Eindhoven had been linked with a move for the Dutchman last month, but the player has indicated his desire to stay at Highbury and prove himself.
Nantes have warned PSG that they do not want to sell Sylvain Armand - which is seen them turn their attentions to van Bronckhorst and Zenden.
PSG are very keen on the highly-rated defender, but Nantes will do everything to keep the player.
"It is a little boring and destabilizing for him and for the group," Nantes coach Loic Amisse told L'Equipe.
"If the financial income is important, of course it could be good for the club, but then we will have to replace him by a player as strong.
Nantes currently have Egyptian Abou Mossalam on trial, but Amisse is not sure if he would be a adequate replacement for Armand should he leave.
"The Egyptian Abou Mossalam? I don't really know him. Armand is a very important boy for our system as well as for the group life. For me he has not left yet."
