Arsenal attempted to lure the 29-year-old to the Emirates Stadium in June after triggering a release clause in his contract with a £20m bid.
However Vardy, who was away on international duty with England at Euro 2016 at the time, turned down the chance to join the Gunners and instead committed his future to the Premier League champions by signing a new four-year deal.
In an exclusive interview with Sky Sports News HQ, Vardy said he never held talks with Arsenal during that period and insists he still has “unfinished business” with Leicester.
“It’s not been put out there that I have always said the boys, the close-knit brotherhood, is unbelievable and for me, there’s a lot of unfinished business here,” he said.
“I feel that the club is only going one way and that is forward, that’s why I want to be a part of it.
“It wasn’t that big [the decision] when I think about it. It was quite easy and this is where I want to be.”