The Gunners have already submitted a £20 million bid for 24-goal striker Vardy which allegedly activates a release clause in the 29-year-old's contract, and the England man is weighing up where he feels his future should lie.
Ex-Leicester defender Gerry Taggart claimed on Monday it would be catastrophic for the club if Vardy chooses to leave as his exit could leave to an exodus amongst the club's brightest stars.
It appears as though those fears could have some foundation as new reports have suggested that Arsenal are also keen on bringing PFA Player of the year Mahrez to the Emirates Stadium.
The Algerian racked up 17 goals and 11 assists in his stunning debut season in England, and along with Vardy was the source of virtually all that was good in the attacking third of the pitch for the champions as they won the title.
Lineker, who began his career at Leicester and remains a passionate supporter of the club, and also played with distinction for Arsenal's local rivals Tottenham Hotspur, clearly has no time for the Gunners' pursuit of the East Midlands club's prized assets.
Arsenal are now allegedly pursuing Mahrez as well as Vardy. Oh just bugger off?— Gary Lineker (@GaryLineker) June 7, 2016
He tweeted: "Arsenal are now allegedly pursuing Mahrez as well as Vardy. Oh just bugger off?"
It remains to be seen how many of Leicester's stars will still be at the club when the summer transfer window closes in just under three months' time.
However, recent developments have been ominous for the club as they face the unprecedented challenge of beginning a season as defending champions and Champions League competitors next term.