Arsene Wenger targeted the France international in 2017, only to see late approaches knocked back prior to the transfer deadline passing.
Interest may, however, be rekindled once a new man takes the helm at Emirates Stadium.
Lemar, as a 22-year-old talent, remains a solid option for several suitors for the present and future, with Pires of the opinion that he could be heading to England after World Cup 2018.
He told bwin: “Thomas Lemar will leave Monaco after the World Cup this summer.
“I think he needs a new challenge and would love to experience a new country.
“Arsenal were of course interested last year but I don’t know if that’s still the case now that Arsene Wenger will no longer be manager. He would be suited to the Premier League.”
Lemar may not be the only star turn swapping Ligue 1 for the Premier England when the transfer window re-opens.
Pires expects there to be a scramble for the 24-year-old if he is made available, with his qualities making him an attractive option for clubs around the world.
He added: “I think Lyon will receive offers from clubs across Europe for Nabil Fekir this summer.
“He has a lot of quality. He’s fast, he’s strong and he has a lot of quality.
“He has a profile that would fit the Premier League very well and I would be surprised if there weren’t attempts to sign him this year.
“Lyon have a fantastic academy and they are the best club for young players.”