Arsene Wenger is understood to have made Lemar one of his primary transfer targets following the capture of Alexandre Lacazette, but the Gunners have seen bids of £30m, £40m and £45m turned down already.
The Premier League outfit were reportedly still hopeful of completing a deal for the 21-year-old, but Vasilyev has ruled out the possibility of letting the youngster go.
"We have kept all of the key players that we intended to keep," he told reporters.
"I will address speculation relating to the case of Lemar. He is staying with us. He is an immense talent and is essential for the team."