That was something they weren't able to agree on, so Trotz resigned as coach of the Capitals on Monday.
Trotz was under contract for two more seasons after winning the Stanley Cup with Washington this season triggered a two-year extension clause. But general manager Brian MacLellan said the Capitals accepted Trotz's resignation, leaving him free to coach elsewhere.
Other than the Capitals, the only NHL team without a coach is the New York Islanders.
Whether other teams rethink their coaching situation now that Trotz is available remains to be seen. It would be understandable if some do.
[RELATED: Trotz leaves as coach of Capitals]
Trotz, who will turn 56 on July 15, has an impressive resume. He's less than two weeks removed from coaching the Capitals to the first Stanley Cup championship in their 43-season history. He is fifth in NHL history with 762 wins (762-568-134 with 60 ties) and fifth in games with 1,524.
Two of the four coaches ahead of Trotz on those lists -- Scotty Bowman (1,244 wins, 2,141 games) and Al Arbour (782 wins, 1,607 games) -- are in the Hockey Hall of Fame. The other two -- Joel Quenneville (884 wins, 1,621 games) and Ken Hitchcock (823 wins, 1,536) -- likely will be someday.
Video: Barry Trotz resigns as Capitals head coach
So if new Islanders GM Lou Lamoriello doesn't think Trotz is the right fit, some other GM eventually will, whether it's now or at some point during next season. Then, Trotz will learn if that team will give him what the Capitals wouldn't.
MacLellan said Monday that the main sticking point in talks with Trotz's agent was that he wanted a five-year contract. The Capitals weren't willing to go that far.
MacLellan acknowledged that salary also was an issue.
"There's probably four guys that are making that kind of money," he said. "It's the upper echelon. It's the big-revenue teams."
It's not difficult to figure out which coaches MacLellan was talking about: Toronto Maple Leafs coach Mike Babcock, who won the Stanley Cup with the Detroit Red Wings in 2008 and has coached in the Stanley Cup Final two other times; Quenneville, who has won the Cup three times with the Chicago Blackhawks; and Montreal Canadiens coach Claude Julien, who won the Cup with the Boston Bruins in 2011 and reached the Final again with the Bruins in 2013.
MacLellan didn't dispute that Trotz deserves to be considered in that echelon, but it's clear the Capitals didn't want to pay him at the same level, at least not for five seasons. MacLellan hoped to work out a shorter-term deal.
"I don't know that there's an easy solution to it," MacLellan said. "He's done a great job here, won a Cup, and we'll see if he gets that contract somewhere else."
That Trotz wanted long-term security isn't surprising after he worked this season without it on the final year of the four-year contract he signed May 26, 2014.
Although Washington won the Presidents' Trophy in 2015-16 and 2016-17, it lost to the Pittsburgh Penguins in the Eastern Conference Second Round each season. Because of that, the Capitals decided not to give Trotz an extension last offseason, creating a potentially uncomfortable situation between Trotz and associate coach Todd Reirden, his likely successor who is signed through 2018-19.
When the Capitals went 10-9-1 in their first 20 games, it looked like MacLellan might make a coaching change, but the Capitals turned their season around by going 17-4-2 in their next 23 games and went on to finish first in the Metropolitan Division for the third consecutive season.
Although Trotz said last week that he didn't think he needed to win the Stanley Cup to cement his legacy, what he did with Washington this season was his crowning achievement in 19 seasons as an NHL coach -- the first 15 with the Nashville Predators and the past four with the Capitals. Not only had the Capitals never won the Cup, but they had reached the Stanley Cup Final only once previously, in 1998, when they were swept by Bowman's Red Wings.
Before their run this season, the Capitals hadn't advanced past the second round since 1998. Trotz also had never advanced beyond the second round in his previous 18 seasons in the NHL.
So getting over that second-round hump and winning the Cup exorcised a bunch of Stanley Cup Playoff demons for the Capitals and Trotz.
Video: Tom Gulitti on Barry Trotz resigning from Washington
Next season, the Capitals will learn how much they needed each other to do it. Their bid to repeat as Stanley Cup champions, with Reirden or someone else as coach, might depend on it.
"The best thing he did in my mind here is he changed the culture," MacLellan said of Trotz. "He came in and did a great job with it. I think what he and his staff and the players have established is here now, and it's our job to find a guy that can maintain it as a group too.
"It's just not one person that maintains that culture. I think our players have grown and adapted and are at a level now, or our room is at a level now, where we can take on some change."
Adapting to that change is another challenge the Capitals will have to overcome next season while Trotz potentially blazes his own path.
If it's with the Islanders, Trotz's path could intersect with the Capitals' in the postseason, which would add another chapter to this story.