The 23-year-old Monaco player can function as either a right-back or centre half.
Arsene Wenger has been keeping tabs on Tisserand, as he seeks to bolster his defence with Per Mertesacker and Gabriel both injured.
New signing Rob Holding has been marshalling the defence and played in the goalless draw away to the reigning Premier League champions Leicester on Saturday.
Recent reports had suggested that the Gunners had added Tisserand to their summer wishlist.
The Daily Mirror claim that the north London outfit have made an enquiry for his services.
However, it is also suggested that the player has put a move to Espanyol on hold in the hope Arsenal firm up their interest.
The board and Wenger have let Arsenal fans down again!
Besides Espanyol, French side Saint-Etienne are also monitoring his situation.
Arsenal have been chasing Valencia's Shkodran Mustafi, although he may be out of their budget as he would cost £50m.