"I believe Leicester should offer him a bumper new deal and kick on from there,” said the former Arsenal striker. "When you look at the way he plays, he's not somebody who looks like he's not going to give his all."
"I am sure at some stage people will say there's bigger clubs knocking on the door," added Wright. "What you're hoping is he does as well as he can and if an offer comes from a top-four club, he has that decision to make.”
Vardy has been on the books of Leicester since 2012 and has been in sensational form so far this season.
The 28-year-old striker has scored 12 goals and created 15 chances in 12 Premier League appearances so far this campaign.
The former Fleetwood Town man has a pass accuracy of 66% and a shot accuracy of 59%, and has won 39 headers, 11 dribbles and 15 tackles.
Vardy’s form this season has also led him to earn four caps for the England national team.
Leicester are third in the Premier League table at the moment with 25 points from 12 matches.
Claudio Ranieri’s side are just a point behind leaders Manchester City and Arsenal, who are first and second respectively.
The Foxes will take on Newcastle United away from home at St. James’ Park in the league on Saturday afternoon.