Sullivan said Friday he met with Malkin earlier this offseason.
"I think the specifics of the conversation we'll keep between [Evgeni] and I, but certainly, we're very much on the same page as far as how we're going to go moving forward," the coach said. "He's an elite player. He'll continue to be an elite player in this league. He's been one of the best players of his generation, and he'll continue to be that for us."
Sullivan applied that same level of confidence to the Penguins roster, which has been slightly retooled since they finished third in the Metropolitan Division and were swept by the New York Islanders in the Eastern Conference First Round.
Pittsburgh received Galchenyuk and defenseman prospect Pierre-Olivier Joseph in the trade for Kessel, acquired forward Dominik Kahun from the Chicago Blackhawks in a trade for defenseman Olli Maatta, and signed free agent forward Brandon Tanev from the Winnipeg Jets to a six-year contract with an average annual value of $3.5 million.
"I'm excited about the group of players that we have," Sullivan said. "We believe we have a group that has the potential to be a very competitive hockey team. Now the challenge is, for all of us that are part of it, to come together and bring that to fruition. But we certainly like the group that we have."
After their season ended, Penguins general manager Jim Rutherford publicly considered if the players became content after winning the Stanley Cup in 2016 and 2017, Sullivan's first two seasons as coach.
Sullivan said the recent changes will improve Pittsburgh's perceived lack of chemistry.
"We just felt that, as a group, we didn't come together the way we should have or could have in order to maximize the potential of our group," he said. "I think part of what excites us moving forward is the enthusiasm that some of the new players acquired have expressed to us ... how excited they are with the opportunity in front of them to become part of the Pittsburgh Penguins organization and become part of a group that potentially has a chance to win Stanley Cups."
Sullivan will be signed to coach through the 2023-24 NHL season. The 51-year-old is 174-92-34 since he was hired Dec. 12, 2015, to replace Mike Johnston.
Sullivan's 300 games coached and 174 wins each rank third in Pittsburgh history. He is 216 games behind Eddie Johnston and 78 wins behind Dan Bylsma for first place.
"[Leaving Pittsburgh] was never really something I ever really considered or thought of," Sullivan said. "I just knew that I wanted to be the coach of the Pittsburgh Penguins."