The 39-year-old left English football last summer to sign for Italian side Cremonese, where he scored seven times in 29 Serie A appearances last season but could not stop the club from being relegated.
Vardy is now a free agent, and with the season fast approaching, he will be in search of a new club that is in need of not only attacking reinforcements but experience that can set an example to a squad of players.
With 145 goals to his name in the English top flight, the Premier League winner has been linked with West Ham this week as per The Sun and GB News, who report that the Hammers are keen on the veteran.
According to Sky Sports News, West Ham are "keeping an eye" on Vardy's situation as they aim to add him alongside Jarrod Bowen, who committed to staying at the club despite their relegation from the Premier League.
Speaking recently about whether he has any plans to hang up his boots, he admitted: "No, I’m not going to give up playing just yet, but it’s something more for later down the line."
A potential move for Vardy comes as Niclas Fullkrug has been left without a squad number following his return from a loan spell at AC Milan, suggesting his time with the side is over.
West Ham’s Championship promotion challenge begins as they travel to Burnley on Sunday, a test which Vardy might well be keeping an eye on.
As the summer transfer window ramps up, Flashscore has everything you need to keep up with breaking news, rumours and analysis. Follow our live transfer blog to follow the biggest moves, whilst expert Dean Jones will be on hand to provide the inside stories from around the world.