Those bids were also rejected by the principality club, before they eventually accepted a Deadline Day bid of £92million from Arsenal.
"No games now so I hope you can enjoy the next five or six days with all the rumours and all that stuff".
Report in England suggested that Liverpool had moved ahead of Arsenal in the race to sign Lemar on Wednesday as Jurgen Klopp looked to further bolster his attacking options.
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It is believed that the youngster "preferred a move to Liverpool to play in the Champions League", according to Sky Sports.
"I am a player of Monaco, I am very happy there", Lemar, who joined from Caen for less than €4m in 2015, told Canal+.
Asked where he would be going once the current worldwide get together was over, Lemar added that he would be Monaco bound.
Monaco subsequently fielded interest in several players on the back of that campaign, with Tiemoue Bakayoko, Benjamin Mendy, Bernardo Silva and Kylian Mbappe all departing.