The 29-year-old fired Leicester City to a fairytale Premier League title this past season by netting 24 goals - one less than Golden Boot recipient Harry Kane.
The Gunners are widely believed to be in the market for a striker after Olivier Giroud - who netted 24 times in all competitions - went 15 league games without a goal in the second half of the 2015-16 campaign, hindering Arsenal's title hopes in the process.
And Sky Bet suggest that Vardy - who is set to represent England at Euro 2016 - is certainly on manager Arsene Wenger's radar.
With that being said, Wenger, who has already splashed some £35 million on signing midfielder Granit Xhaka this summer, may not spend big money on a player of Vardy's age.
The Leicester ace will turn 30 in January and Wenger, as every manager does, often takes age into account with his transfer policy, be it signing players or keeping them at the club.
Manchester United are priced at 20/1, while Manchester City and West ham United are 28/1 and 25/1 respectively. He is 5/6 to stay with the Foxes.