The Italy midfielder sustained an ankle injury in the 9-0 hammering of Guingamp on January 19 but, although he was declared unfit for Wednesday's Coupe de France win at Villefranche due to another ailment, came through training on Thursday and seems likely to play at the weekend.
Assuming there are no further complications, that would put Verratti firmly in the frame to face Manchester United in the first leg of the Champions League last 16 tie at Old Trafford on Tuesday.
Tuchel told a news conference: "Marco trained on Thursday and there is no problem.
"I'm waiting for the afternoon training [on Friday] but he's available to play against Bordeaux. Maybe not 90 minutes, we'll talk with the physio, the doctor and the player but I think he can play.
"I do not know yet if it's possible, we have to wait."
PSG have been forced to play defenders Marquinhos and Dani Alves in midfield in recent weeks with Verratti injured and Adrien Rabiot out of contention due to a contract dispute.
With Ligue 1 table-toppers PSG 10 points clear of second-placed Lille, and with two games in hand, Tuchel will make several changes for the visit of Bordeaux to the Parc des Princes.
He added: "It is not possible to just let go of the match against Bordeaux but it is my responsibility to protect players who have played a lot in recent weeks.
"Maybe some of the players who have not played too much will play."
The German admitted his focus was on the midweek trip to Manchester.
"Of course, everyone thinks about Manchester but we have to think about Bordeaux," he said. "We talk about it [United] but in a calm way. The squad knows how to do one thing after another.
"I know 10 players who will play against United. Then you have to stay flexible."