Everton are on the lookout for a new manager following the departure of Roberto Martinez from Goodison Park last week.
According to a recent report in The Daily Mail, Everton are interested in appointing Koeman as the new boss.
Former Arsenal striker Wright has suggested that the Toffees would not be able to match the ambitions of the Dutchman.
The former England international has also claimed that leaving the Saints for Everton would not be a step-up in his managerial career for Koeman.
“If he leaves to go to Everton, can Everton match his ambitions?” quipped Wright on The Sun Goals Podcast.
“In this day and age, from what I saw under Martinez, I am not sure it is,” added the Englishman when asked if leaving Southampton for Everton would be a step-up.
Southampton finished above Everton in the Premier League table this season and will play in the Europa League during the 2016-17 campaign. It would be best for Koeman if he remains at St. Mary’s Stadium for one more season.