Vardy has reportedly been the subject of a £20m bid from Arsenal.
The 29-year-old's representatives have told the Gunners that Vardy wants to focus on Euro 2016 at the moment.
"I have spoken to Jamie. Everyone wants him to stay. We would like everyone to stay, even if it's just for one more year," Simpson told BBC's Sportsweek.
"It's his decision, and he says he wants to concentrate on the European Championships. Jamie knows what I think of him as a lad and a player.
"No money can buy the bond that we have got at the club. It's a special group. Why not carry on and kick on as a group and squad?"
Simpson, 29, felt England manager Roy Hodgson should have included Vardy in his starting line-up for their Euro 2016 opener with Russia, which ended in a 1-1 draw.
"I was disappointed he didn't start never mind that he didn't come on. I am sure he will get an opportunity soon," Simpson added.
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Leicester City defender Danny Simpson has urged England striker Jamie Vardy to stay with the Premier League champions.