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.
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.”