Lemar, 21, was heavily linked with a move to the Premier League during the summer transfer window.
Both Liverpool and Arsenal lodged bids to sign the France international as they looked to bolster their ranks.
It appeared as if Arsenal had won the race to sign the France international after lodging a £92million deadline day offer, which Monaco accepted.
But Lemar snubbed their advances in favour of staying with the Ligue 1 champions.
This subsequently resulted in Alexis Sanchez’s move to Manchester City collapsing after they failed to land their top target.
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However, Monaco chief Vasilyev has revealed Lemar was in favour of moving to the Premier League and signing for both Liverpool and Arsenal.
“It was not easy. Thomas wanted to go to Arsenal and to Liverpool, but we had discussions and we took a communal decision so that he could stay here,” he said.
“He is a very important player for us.
“We could not have sold him, it would have affected the entire team and the individuals.”
Monaco’s star-studded squad was raided of Kylian Mbappe, Bernardo Silva, Benjamin Mendy and Tiemoue Bakayoko.
But they have spent well by bringing in the likes of Keita Balde, Youri Tielemans and Stevan Jovetic.
Lemar is contracted to Monaco until the summer of 2020.