But it is PSG that appear to have won the race for the 18-year-old, with reports in France having claimed that Unai Emery's side have agreed a €180 million deal with Monaco.
He told reporters: "He's [Mbappe] changing clubs but staying in Ligue 1. The future will say if he's made a good decision."
Deschamps has also appeared to go back on his word that players wouldn't be allowed to undergo medical examinations with prospective new clubs whilst on international duty.
The 48-year-old had suggested that anyone called up would have to have sorted their transfer situation before joining up with the squad, but now says that medicals within the France set-up are possible.
He added: "Players will remain here [during the international break]. [Can they] pass the medical examinations here? Yes, it's possible."
Mbappe hasn't featured for Monaco since the first game of the Ligue 1 season and was an unused substitute in his side's 6-1 demolition of Marseille on Sunday.