There has been concern over Mbappe's availability since he suffered a broken nose in Monday's 1-0 win over Austria in Dusseldorf.
Blood was seen pouring from the forward's nose after his face collided with the shoulder of Austria centre-back Kevin Danso.
Mbappe was subsequently replaced by Olivier Giroud in the 90th minute and was seen leaving the stadium in an ambulance.
Deschamps hints at Mbappe invovlement
France had already confirmed that Mbappe would not require surgery, but there has been doubt surrounding his availability ahead of Friday's game in Leipzig.
However, Deschamps has indicated that the 25-year-old could be involved in the second group match, revealing that he is making progress in his recovery.
Speaking to reporters on Thursday, Deschamp said: "Everything is going in the right direction after this major shock with the consequences.
"Yesterday he went out, he did a little activity. This will also be the case this evening. Things are moving in the right direction to ensure that he is available tomorrow."
If Mbappe is unable to feature against the Dutch, Deschamp may turn to the experience of France's all-time leading scorer Giroud.
Mbappe set to don mask on return
Mbappe was pictured in training on Thursday wearing a mask in the tricolour colours of the French flag as well as featuring his initials and shirt number.
Deschamps has confirmed that Real Madrid's summer signing will be sporting a custom-made mask when he returns to action.
The France boss added: "Kylian will be wearing a mask, yes, we don't really need to know the details about this mask. I think you have enough moles to find out where the mask is coming from anyway."
However, Mbappe will be unable to wear the same mask he wore in training as UEFA rules state that it must be of a single colour.
The 2022 World Cup finalists will progress to the last 16 with a game to spare if they beat the Netherlands on Friday.