You can bet that many Lightning fans hoped Senators superstar defenseman Erik Karlsson jumped on Tampa Bay's bus after Thursday night's 4-3 Lightning win.

Karlsson, 27, a two-time Norris Trophy winner, is the biggest prize leading up to Monday's trade deadline.

"I don't think there's a team in the league that would say no to a world-class player like that," said Lightning defenseman Victor Hedman, Karlsson's good friend and fellow Swede.

Turns out, the Lightning might be saying no to the price for Karlsson.

General manager Steve Yzerman said Thursday he's not sure what, if anything, he'll be able to accomplish by the deadline, saying there are a "very limited" amount of fits so far in terms of what the Lightning wants to do.

And that Yzerman said he doesn't plan to deal from his current roster – including young core players such as Brayden Point and Mikhail Sergachev – makes it unlikely Tampa Bay will have the king's ransom Ottawa would demand for its franchise player.

RELATED: Lightning escapes with 4-3 win over Senators.

"At the trade deadline, when you're trying to acquire players, usually teams that are selling are looking for younger players, draft picks and prospects," Yzerman said. "At this stage, the young players (we have) on our team we want to keep on our team, and we want to add to that.

"We're trying to keep this team together with the hope of improving it."

There's no guarantee the Senators will move Karlsson by Monday. It could wait for this summer's draft, where more teams might be in the bidding. But the Lightning is among the teams that have kicked the tires on Karlsson.

The Lightning has other options as it hopes to address its blue line. There's Rangers captain Ryan McDonagh, 28, a shutdown defenseman who has another year on his contract at $4.7 million. McDonagh has a 10-team no-trade list, but the Lightning isn't on it. Tampa Bay could be a match if the price is right.

Tampa Bay could also target pending unrestricted free agent Mike Green in Detroit. Columbus left-shot Jack Johnson, a pending unrestricted free agent, seems like a good fit, but the sports-news website The Athletic reported Thursday the Blue Jackets have began engaging in contract-extension talks with the veteran defenseman.

When I asked Yzerman today if he felt he was in position to make major move or more likely a depth deal, he declined to go there. We’ll see. — Joe Smith (@TBTimes_JSmith) February 23, 2018

The Lightning has all of its draft picks for the next three seasons and a deep prospect pool including defenseman Cal Foote and forwards Taylor Raddsyh and Brett Howden. But Yzerman isn't going to give up the farm – for Karlsson or anyone else – noting there's no guarantee a Stanley Cup would be the reward.

Keep in mind that if Tampa Bay acquired Karlsson, it'd probably be for just 1 1/2 years, as he'll likely demand between $10 million to $12 million annually as a free agent in the summer of 2019.

"I really don't want to just get a player or something at all costs," Yzerman said. "I don't believe in that. Obviously, if we feel we can improve our team and it gives us a better chance to be more successful in the playoffs, that would be our goal.

"I may not be able to do that."

Yzerman plans to stay in Tampa this weekend through the deadline as he explores his options. The Lightning holds a one-point lead in first place in the Atlantic Division over the surging Bruins, and is trying to work its way through a midseason lull.

RELATED: Flashy moves not always the smartest ones at trade deadline.

"There are some encouraging aspects and some areas that still stick out there we need to improve on," Yzerman said. "In speaking with (coach Jon) Cooper and our players, they're working on those things.

"We're not totally satisfied with the way we're playing and recognize we need to improve in certain areas. The schedule we have moving forward allows us more practice time, which will be beneficial to our team when we're working through something like this."

Lightning players have said it's exciting to see what Yzerman might do at the deadline, but Hedman said they're also "happy with the team we have."

"You want to try to get better," Hedman said, "without disrupting the chemistry and core of this team."

And it sounds like Yzerman doesn't plan on breaking up this roster and would be okay with standing pat.

"If I can't improve the team, we'll go with the team we have," Yzerman said. "I'm good with that."