The France international has been heavily linked with a move to the FA Cup winners in the summer transfer window.
Arsenal boss Arsene Wenger is thought to be keen to sign the 21-year-old to bolster his attacking options as Alexis Sanchez continues to be linked with a summer exit.
The north London side have reportedly failed with three bids to sign the AS Monaco forward but the French champions have rejected Arsenal’s attempts to sign Lemar.
But Monaco manager Jardim admitted that he can not be certain that Lemar will remain at the French club beyond the summer transfer window.
“All the players who were important last season are important to keep for the club,” Jardim told a press conference on Thursday.
“But it has been shown over the years that it’s not always possible to keep the players, and you know how our project works. So our goal is to work well with players who will stay here after the transfer window closes.”
Arsenal were 2-1 winners against Premier League champions Chelsea in the FA Cup final at Wembley back in May.
The Gunners signed Bosnian defender Sead Kolasinac in a free transfer from Bundesliga giants Schalke 04.
The north London side spent a club record £52m fee from Lyon striker Alexandre Lacazette.
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