However, reports emerged yesterday suggesting that the 29-year-old, who scored 24 Premier League goals to help fire the Foxes to the title last season, was leaning towards rejecting the offer.
"It looks like it isn't happening now. I was at the Arsenal the other day and there were big reports flying around, and the club's cameramen and digital staff had to get down to the training ground," Parlour told talkSPORT.
"So it looked like it was going to happen - there was a medical being done. But it seems Vardy thought about it while on England duty, and suddenly there was a U-turn."
Vardy is currently with the England squad preparing for their Euro 2016 opener on Saturday.