Those bids were also rejected by the principality club, before they eventually accepted a Deadline Day bid of £92million from Arsenal.
It's been a insane day for Arsenal, Liverpool and Monaco, with Thomas Lemar in the middle of it.
Wenger declared a deal for Lemar "dead" earlier this month.
Much of these reports began to gather pace as pictures emerged on social media of the Arsenal manager and chief executive Ivan Gazidis in Nice in June.
One source told Sky Sports News that Lemar is not interested in a switch to the Emirates and would prefer to move to Liverpool.
Lovely goal, not what Arsenal fans wanted to see after all that happened today.
Perhaps the only thing clear at this moment is that Thomas Lemar will not transfer to Arsenal today and that the London club will now hold on to Alexis Sanchez-and given how things have gone today, it would be a fearless person willing to bet on even that still being a certainty in another hour.
The Gunners defender played on and Arsene Wenger will be hoping it is not as serious as it initially looked. Lemar scored 16 Ligue 1 goals over the last two seasons, and has done well enough to break into the French national team.
Across the 90 minutes, Lemar created more chances (2.41) than Alexis (2.18) and also achieved a hugely superior defence score (2.75) over the Arsenal forward (0.75); an area of the game which is of huge importance when using the 3-4-3 system as a winger.
Lemar, a 21-year-old French worldwide, set Ligue 1 and the Champions League ablaze last season, with his combination of pace, pinpoint delivery and eye for goal having alerted some of Europe's biggest clubs to his talents.