The Frenchman has been heavily linked with a switch to Barcelona, and though Tuchel said he wants Rabiot to stay, he said he could not guarantee it, per Canal Plus (h/t Goal's Jamie Smith):
"I'm not certain he will stay. I want him to stay, but it's up to him. He has great potential and can improve even further. He can become a top player but has to stay with us."
Rabiot netted PSG's second goal at the Parc des Princes on Sunday as Tuchel made a winning start to his first league campaign in charge.
The 23-year-old has been linked with a departure from PSG for much of the summer, and he is now into the final year of his contract with the French giants.
Per L'Equipe (via French football writer Jeremy Smith), Rabiot recently turned down the offer of a new contract as he is eager to depart PSG:
Jeremy Smith @jeremysmith98
.@lequipe reporting that Adrien Rabiot rejected another improved PSG offer a few days ago. Apparently not a money issue - he just wants to go elsewhere. But club don't want to sell, willing to let his contract run down, leave him on the bench and let him go for free next summer.
He joined the club's youth academy in 2010 and has been a part of the first team in Paris since 2013.
However, the likelihood of Rabiot departing before the transfer window closes at the end of the month looks to be increasing.
Barcelona could still be looking to add another central midfielder to their ranks. They lost Andres Iniesta and Paulinho at the end of the 2017-18 season and, though they have brought in Arthur and Arturo Vidal.
As well as Rabiot, Ajax's Frenkie De Jong has been linked, per Football Espana.
Jason Burt in the Telegraph also recently reported the Blaugrana have not given up on potentially signing Manchester United's Paul Pogba.