The two clubs are consequently a long way apart with Arsenal having an initial bid just below £30m rejected last month.
The Brazilian global made his name as a right-back but excelled after being converted in to a holding midfielder as he played a key role in helping Monaco win the Ligue 1 title last season.
However, Arsenal reportedly face an uphill battle trying to convince Monaco to part with the influential winger.
Mahrez's £50m tag putting Gunners off
Earlier this summer it looked like a straight north London battle between Spurs and Arsenal for Lemar.
Arsenal have made an increased offer for Thomas Lemar worth €45 million (about £40 million), according to L'Équipe.
The Gunners are now way off reaching the French side's asking price and have kicked off negotiations with a £30m bid.
Will signing Lacazette tip Lemar into forcing his way out of Monaco?
Sport Witness cited L'Equipe's report and acknowledged Lemar and Lacazette's friendship as an undeniable factor in the speculation, not to mention there are already a glut of French speakers at the Emirates. Arguing that point seems a stretch right now.
Arsenal believed that £50m is too much for a 26-year-old coming off a reasonable year, which is why they prefer Thomas Lemar.