Vardy scored 24 goals in 36 Premier League matches for the Foxes this season as they won a historic first league title, and he has also become a fully-fledged England international, scoring three goals in his last four caps.
That form is thought to have attracted the interest of several big-name clubs, particularly due to the 29-year-old's reported release clause, and Arsenal appear to be fronting the queue.
The Gunners suffered in attack this season, with Danny Welbeck enduring terrible injury problems, Theo Walcott in poor form, and top scorer Olivier Giroud going nearly four months without a league goal from mid-January.
The North London side have made an offer worth around £20 million for Vardy, who is mulling over his decision as he travels with the rest of the England squad to France ahead of Euro 2016.
Keown, who played 451 senior competitive games for Arsenal, believes Vardy's skill set makes him the perfect signing to bring another dimension to the club's attack next season.
The 49-year-old told 888sport: "If you look at Vardy and you look at what Arsenal don’t have down the middle with their strikers – someone who likes to run behind a defence – then if you feed him he’s a real handful and as good as anyone.
"He’d be a player who would strengthen Arsenal and give them more variation to their play which they lack down that central area."
Vardy would certainly appear - on paper, at least - to be the missing ingredient for Arsenal as they attempt to sustain a title challenge next season and win a first championship since 2004.
However, his rise has been rapid, and former Premier League midfielder Jason McAteer warned top clubs on Monday that they must be cautious in placing too much faith in the stars of Leicester's incredible season.