Experienced full-back Evra had his contract with the Ligue 1 side terminated after being suspended from UEFA competition until the end of this season for kicking a supporter.
The 36-year-old was red carded before the start of Marseille's 1-0 Europa League defeat at Vitoria Guimaraes this month after an altercation with a group of travelling fans boiled over.
A section of OM supporters held up a banner with the words "Evra get out" during their 5-0 win against Caen last weekend.
Evra started every match as France finished as runners-up at Euro 2016, and Deschamps said he would send the defender a private message rather than issue a public statement.
"I will not go through you [the media] to give him a message. To give him a message I will do it directly, as I have always done.
"His situation is very complicated and I wouldn't wish anyone to be in this situation.
"But these actions have happened. They are there, they are heavy."