Advocaat took charge of the Black Cats in March and has guided them to Premier League safety, creating a strong bond with the players at his disposal.
Fletcher believes that the Dutchman has laid the foundations for whoever takes over to be a success, and the Scottish striker insists that whoever inherits the reins should not look to change too much when they first arrive.
"Whatever manager comes in needs to rebuild the team," he said. "A few players will obviously go and it's just important that any new manager that comes in creates the same mentality as what the gaffer has done."
Sunderland had looked doomed at one point in the season, so the job that Advocaat has done at the Stadium of Light cannot be underestimated.
He took the Black Cats post at a point when they looked to be low on confidence under Gus Poyet, but the 67-year-old managed to find a way to get them winning again.
Sunderland often utilised defensive tactics away from home, but their solidarity helped to get them over the line.
Big wins against Newcastle United and Everton were followed by a draw against Arsenal, and that run of form has meant that they will remain a top-flight outfit for the 2015/16 campaign.