Pittsburgh failed in its attempt to win the Stanley Cup for a third straight season when it was eliminated by the Washington Capitals in the Eastern Conference Second Round. Afterward, reports surfaced that Kessel, who scored one goal in 12 Stanley Cup Playoff games, was unhappy being taken off a line with center Evgeni Malkin.
"That's not true," Sullivan said. "Where did that come from? Who said that? Phil played a lot with Geno. Phil played most of the [first round series against the Philadelphia Flyers] with Geno.
"We think our team is at its best and has a competitive advantage when we create balance throughout our lineup. Sometimes that means we spread our stars. But we don't always spread our stars. ... It's not like [Phil and Evgeni] don't get the opportunity to play together."
Pittsburgh general manager Jim Rutherford said June 11 that he did not intend to trade Kessel and believed his relationship with Sullivan would be worked out.
"I think our relationship has grown because we've been through ups and downs," Sullivan said. "That, for me, is the process of coaching: coach-to-player relationships.
"I have so much respect for Phil as an athlete and person. I really like Phil. I value the relationship that we have.
"Have we had ups and downs through the course of three years or differences of opinions in certain situations? Of course. I think you could say that coach-to-player in a lot of situations. My commitment to our players is always to try and find common ground. Phil's no different."
Kessel, who turns 31 Oct. 2, had an NHL career high 92 points (34 goals, 58 assists) this season. He has 221 points (83 goals, 138 assists) in 246 games with Pittsburgh and has played every game since 2010-11, when he was with the Toronto Maple Leafs. He has four years remaining on his contract.
"Phil's a great, competitive teammate, and he wants to help the Penguins win," Sullivan said. "Him and I have a very candid relationship. Do we always agree on how we utilize Phil? No we don't. For the most part I think there's a mutual respect between this coaching staff and Phil in what we're trying to accomplish."