The England international insists that a transfer was never really on the cards even though it was believed that Arsenal had triggered his release clause prior to Euro 2016.
"[Turning down Arsenal] wasn't that big when I think about it. It was quite easy and this is where I want to be," Vardy told Sky Sports.
"I was away with England so [a move to Arsenal wasn't close]. No [I didn't speak to them.]
"There's a lot of unfinished business here. 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."
Vardy ended up signing a contract extension with the Premier League champions and is hoping that Riyad Mahrez will do the same and stay with Leicester.
"I think everyone in the squad would want him here, playing with us," Vardy added.
"But that's nothing to do with us and it's down to Riyad and the club to sort out."