Thomas Lemar was interested in joining either Arsenal or Liverpool, according to Monaco's vice president Vadim Vasilyev.
Arsenal's club record bid of £92m for Lemar was accepted by the French champions, but Arsene Wenger claimed that Lemar rejected the move because he wanted to stay in France.
Speaking to Sky Sports, Vasilyev said: "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."
Wenger said on Sunday that Arsenal may potentially look at Lemar again in January but could face competition from Liverpool who had two bids rejected.
Lemar, though, is still a key player for Monaco with Vasilyev saying: "He is a very important player for us. We could not have sold him, it would have affected the entire team and the individuals."
The 21-year-old has three years left on his current Monaco contract and enjoyed a stellar season in 2016/17.
He scored 14 goals in 55 games, while also providing a number of assists as Monaco won the Ligue 1 title for the first time in 17 years. He has also started the new season well, scoring a screamer as France beat the Netherlands on Thursday.
Monaco have started the defence of their Ligue 1 crown superbly with four straight wins including an eye-catching 6-1 triumph over Marseille.
They face Nice away in their next match on Saturday before they return to Champions League action with a trip to Germany to battle with RB Leipzig.