The former Juventus coach has allegedly made the decision to throw in the towel after a disappointing 2011-12 campaign with les PhoceensOlympique de Marseille, L'Equipe and La Provence report.
Marseille resumes training ahead of the 2012-13 campaign on July 2, but it will do so without the former Monaco and Juventus boss, who has opted to step aside.
Deschamps feels the club are showing a lack of ambition after a disappointing 2011-12 season, where les Phoceens had to settle for 10th-place finish in the Ligue 1 table.
He also endured a troublesome relationship with sporting director Jose Anigo, and has told chairman Vincent Labrune that he has no intention of honoring his contract, which was due to run until June 2014.
Marseille has yet to accept Deschamps' resignation, but it appears to be a matter of time until the former France international's departure is official.
The 43-year-old is believed to be one of the candidates to replace Laurent Blanc as France coach after Euro 2012, and has also been linked to the vacant post at Tottenham Hotspur.