But he should. And the conversation should center on goaltending and how the two teams can help each other.
After all, one of the reasons why the Lightning have the sixth overall pick at the June 25 NHL Draft in Los Angeles is goaltending, or the lack thereof.
And goaltending is the one issue that is front and center in Montreal where playoff hero Jaroslav Halak, pictured at left, and his back-up, Carey Price, pictured right, both want to be starters next season. And you just know neither would really be in favor of sharing the net.
"It would be pretty tough," said Price as he cleaned out his locker earlier this week after the Canadiens were eliminated from the Stanley Cup playoffs. "I feel like I can play and I know Jaro definitely feels the same way. It's a tough situation for both of us."
"We've got two young goalies. I'm sure management will do its best to give us both a chance to play."
So what we have here is two teams that could help each other.
Yzerman has two pillars to build his team around in 50-goal-scorer Steve Stamkos and towering Victor Hedman on defence.
But when it comes to goaltending, the Bolts are in need of an upgrade.
Mike Smith had a 3.09 goals-against average and a .900 save percentage in 42 appearances for the Lightning this season, while Antero Niittymaki had a 2.87 goals-against average and a .909 save percentage in 49 appearances.
That's not what you call strength in net.
Both Halak and Price can become free agents this summer and Gauthier said both are "assets we could protect," should another team produce an offer sheet.
In other words, one is likely to be traded.
Price earned $850,000 and isn't in a great bargaining position to hit the proverbial home run in hiking his wage scale. He didn't exactly help himself this season with his performance on and off the ice.
Halak made $800,000 and, given his playoff performance, is in a much better bargaining position for a considerable raise.
The Slovak goalie had a 2.40 GAA and a sparkling .924 save percentage in the regular season and the Habs would not have made it to the Eastern Conference Final without him. He boasted a 2.55 goals-against average and a .923 save percentage in the playoffs.
Halak is eligible for arbitration, another potential bargaining chip in his arsenal.
It's obvious Gauthier has a decision here to make, and that's which goalie to sign and which one to trade.
Does he trade Halak to make room for Price or deal Price and pass the crown to Halak?
Halak is 25 and entering the prime years of his career as a goaltender. While some people might suggest his playoff heroics were a fluke, they should look back to his performance at the Vancouver Winter Games. The Slovaks surprised by finishing fourth and Halak was the guy between the pipes.
When the Canadiens made Price the fifth overall pick in 2005, they thought they solidified their netminding for years to come. Price is 23 and is still an infant when it comes to his NHL career.
Does Gauthier cut ties with Price after three seasons and hope that's a trade that doesn't come back to bite him in the butt.
Or does he capitalize on Halak's new-found status as a top-draw goalie?
Either way, Gauthier's got a good problem on his hands. A problem that Yzerman and the Tampa Bay Lightning may be able to help solve.