Arsene Wenger is willing to give the 29-year-old, currently at Euro 2016 on England international duty, time to make up his mind on the deal.
The Gunners boss is said to be understanding of Vardy’s commitment to Leicester, whom he helped to a fairytale Premier League title win last season.
Vardy scored 24 goals to fire the Foxes to glory, continuing his remarkable rise at the club who spotted his talents when he was playing non-league football with Fleetwood Town.
According to the London Evening Standard, Vardy has told England team-mates that he’s 80% likely to remain at the King Power Stadium.
This could be a big blow to Arsenal’s transfer plans, though they are said to be ready to move for Juventus’ Alvaro Morata as an alternative up front.
Leicester have offered Vardy a new £100,000-per-week contract, and his club colleagues have reportedly been in touch to persuade him to reject a move to Arsenal.