Arsenal legend Wright believes that Vardy would be a good signing for the North London outfit.
The former England international striker has also pointed out that making expensive signings from outside the Premier League does not always guarantee success.
Wright has used former Argentina international midfielder Juan Sebastian Veron as an example to prove his point.
Veron joined Manchester United from Italian club Lazio in the summer of 2001 for a transfer fee reported by BBC Sport at the time to be £28.1m.
The Argentine was expected to be a huge success at Old Trafford, but he failed miserably and moved to Chelsea in the summer of 2003 for a transfer fee reported by BBC Sport at the time to be £15m.
Veron struggled to play well at Chelsea and left the London outfit on a permanent basis in 2007.
“I’m delighted to see Arsene going for an English striker who is a proven Premier League goalscorer,” Wright wrote in The Sun. “And, equally important, someone who is a winner.
“Adding Jamie to the side would give the Gunners another dimension, and I believe that at this stage of his career he is ready to blast on and do even greater things.”
“Look at someone like Juan Sebastian Veron,” added Wright. “There was no doubt that when he joined Manchester United, he did so as one of the best midfielders on the planet.
“Yet he only showed it in flashes, even less so when they moved him on to Chelsea, and he left without the Premier League ever seeing his true colours consistently.”
Vardy was one of the best players for Leicester this past season, scoring 24 goals and creating 46 chances in 36 Premier League matches.