The 27-year-old is angling for a return to Spain but reports this week suggest PSG have rejected an offer from Real Madrid of 100 million euros ($111 million) plus players.
Neymar arrived amid deafening fanfare from Barcelona two years ago as the world's most expensive player in a 222 million euros deal.
Barca's own attempt to bring him back to the Camp Nou on loan with an obligation to buy for 160 million euros at the end of the season has also been reportedly rejected in Paris.
Tuchel toyed with reporters on Saturday when asked if his wantaway forward would figure for the first time since injuring his ankle at the end of May.
"He can play (against Toulouse) if the situation between him and the club is clear.....today it's not clear, perhaps tomorrow it will be."
Pressed, the German added that Neymar was "ready to play" but that the final decision rested with the club's sporting director.
"Perhaps you have to speak to Leonardo," he suggested.
"Neymar's had a good week (training) with all the squad, a week with a lot of work and intensity."
The transfer window closes in France, Spain and Italy on September 2, meaning time is fast running out for a deal to be done.