Thomas Lemar was interested in joining Arsenal and Liverpool, according to Monaco vice president Vadim Vasilyev.
The Gunners' £92m club-record offer for Lemar was accepted by Monaco on Deadline Day but, according to manager Arsene Wenger, the France international rejected a move to the Emirates to stay at the Ligue 1 side.
Wenger said on Sunday Arsenal would come back in for Lemar, although they could face further competition from Liverpool, who had two bids for the 21-year-old winger turned down during the summer transfer window.
"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," Vasilyev told TASS.
"He is a very important player for us. We could not have sold him, it would have affected the entire team and the individuals."
Lemar scored 12 goals in 39 appearances last season as Monaco won the Ligue 1 title for the first time in 17 years.
He has three years remaining on his current contract.