PSG face Atalanta in a one-legged tie in Lisbon on August 12 and Tuchel, while not completely ruling Mbappe out, concedes it is almost certain he will be without the striker.
"We still have hope and every day counts to achieve a miracle," Tuchel said at a news conference ahead of PSG's Coupe de la Ligue final with Lyon on Friday.
"But tomorrow we will be without him and his absence will have an influence on us. I hope that a solution can be found."
Thilo Kehrer and Colin Dagba are expected to miss out against Lyon, while Juan Bernat remains doubtful, but Marco Verratti will be hopeful of earning a recall to the side.
Tuchel left Verratti on the bench for 75 minutes last week, instead preferring Leandro Paredes alongside Idrissa Gueye, and has hinted he may again elect for a 4-4-2 on Friday
"It was a super complicated decision to leave Marco on the bench, but I felt I deserved to let Idrissa and Paredes play together after the Borussia Dortmund result," he said.
"If we do keep our 4-4-2, we can do that with Eric Maxim Choupo-Moting, Angel Di Maria or Pablo Sarabia.
"We can make the decision tomorrow. I want to wait until after the final training session."