However, Penguins general manager Jim Rutherford continues to talk to other teams about Kessel, TSN's Pierre LeBrun reports, who adds that it's a question of when - not if - Kessel is dealt.
Rutherford has said publicly he's willing to shake up his roster, while Kessel's name has frequently been mentioned in rumors.
Kessel helped the Penguins win back-to-back Stanley Cups in 2016 and 2017, but the team was swept out of the first round by the New York Islanders this postseason.
The 31-year-old has three years remaining on his current eight-year deal and carries an annual cap hit of $8 million.
In terms of what the Penguins can expect in exchange, it's believed that talented winger Jason Zucker would be part of the trade, reports Yohe. The 27-year-old's speed would fit the Penguins' run-and-gun style and he's hit the 20-goal mark in four of the past five seasons.
Kessel - a Madison, Wis., native - played one season with the University of Minnesota in 2005-06 before turning pro.