Arsenal made their move for the Leicester star two weeks ago, activating a £20milllion release clause in his current contract.
At first it had appeared that a move would be swiftly completed, but the player has left the Gunners waiting on a decision, saying he is determined to focus on his Euro 2016 campaign with England for now.
At this stage his future is very much unknown and Simpson has attempted to sway his decision by urging him to stay at the Kingpower Stadium.
“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,” he told BBC Radio 5 Live.
“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?”
It will certainly be interesting to see what decision Vardy makes when his Euro 2016 campaign with England is finished.
There is no denying that a move to Arsenal must be very tempting, with an offer from one of the other so called big clubs unlikely to come again in future.
At the same time though, he will know he has been a huge success at Leicester and may want to continue that experience as they head into the Champions League for yet another new adventure.