The England international is yet to see a one-year extension on his current deal - due to expire in 2023 - activated by the club.
But Tuchel insists he has no worries about Abraham's future.
"I'm not aware of the contract situations of my players because I don't want to be involved with judging this when I'm making the decisions of who's playing and who's not," Tuchel said, via Goal.
"He deserved to play at Barnsley. He had a difficult game against Burnley at home so he suffered from a tactical shift at half-time and did not play against Tottenham and Sheffield United. That's why he deserved to play because he is a very positive guy, very clear, very ambitious."
The German added: "He played well at Barnsley because he did not only score the decisive goal but was also very important in defensive set pieces, he cleared many situations for us with his head.
"He was absolutely ready to suffer and for that, he has all my credit. It's a good new start for him to step up and show that he is important for us."