The Spanish champions were rumoured to have agreed a deal in principle to sign the French midfielder, who is valued in the region of £35m.
Rabiot has been described as a 'perfect fit' for Barca by club legend Xavi, but it remains to be seen if the 23-year-old will swap one European heavyweight for another before next month's transfer cut-off point.
Asked for an update on Rabiot's future following the 3-1 friendly defeat to Bayern Munich, new PSG boss Tuchel told reporters: "I would love him to stay. Everyone has seen his potential and there's still room to grow.
"In relation to his contract situation, he's the one who has the last word. Everything depends on him. He can stay and adapt to our style or leave the club and try a new experience."
Rabiot was given a 72-minute run-out in the Parisians' opening friendly of the summer.