The Chelsea goalkeeper picked up a rib injury during Sunday’s defeat at Aston Villa and did not appear for the second half.
An X-ray revealed the injury does not appear to be overly serious, raising hopes that Mendy will be available for Saturday’s clash with Manchester City in Porto.
The current plan is for Mendy to return to training on Wednesday along with N’Golo Kante.
But if Mendy is not able to train then, Blues boss Tuchel says he will simply try again 24 hours later and again on the eve of the game if necessary.
Speaking at a press conference, Tuchel explained: “For Edou, the update is that we still have hope that he joins the group.
“He made a huge improvement with the management of pain. We will have a further update on Wednesday.
“Edou will play if he is fit. If he’s not fit on Wednesday we will try on Thursday and we will try on Friday.
“At the same time we have trust that if he cannot make it then we have a strong guy on the bench with Kepa, who will take his place.
“So now the race is on. We are very happy that the images don’t show that the injury is serious, so at the moment we are positive.
“Every hour counts now and every day counts. Hopefully the team around Edou and he himself can do enough and he will be on the pitch.”
Kante, meanwhile, is still expected to overcome a hamstring problem in time to play.
“There is no change with N’Golo. It looks good and I hope it stays that way,” Tuchel said.