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Arsenal have been heavily linked with a move for Lemar after his stunning campaign to help Monaco to the Ligue 1 title last season.
The France international bagged 14 goals and provided 17 assists across all competitions, also helping his side reach the Champions League semi-finals.
But Arsenal are yet to agree a fee with Monaco, who are said to have turned down two Gunners bids for the 21-year-old already this summer.
Monaco vice-president Vadim Vasilyev said earlier this week that Arsenal are wasting their time pursuing Lemar as he’s not for sale.
He said: “We have kept all of the key players that we intended to keep.
“And I will address speculation relating to Lemar – he is staying with us. He is an immense talent and is essential for the team.”
But Wenger has hinted that Arsenal may have to wait to sign Lemar as deals tend to pick up momentum in the final days of the window.
“There’s the usual acceleration in the final part of August,” Wenger said when asked about Arsenal’s transfer plans.
”But I think you have always to be on alert every day, because a good opportunity might turn up.
“Sometimes people you are after for a long time are not available and suddenly they become available. So you have always to be on alert. That’s what we do.”
Arsenal have already spent £52m on striker Alexandre Lacazette this summer, with left-back Sead Kolasinac arriving on a free.