TORONTO — Keith Pelley wants to be as open-minded as possible as he sets out to find the Toronto Maple Leafs’ next head of hockey operations.

But there was a tell in his news conference on Tuesday. Citing the “foundational pieces” he believes are still on the hockey team, the president and CEO of Maple Leaf Sports and Entertainment said he prefers the idea of a retool over a rebuild.

That’s something he 100 percent would have discussed with ownership before announcing it to the world.

Yes, Pelley made sure to add the proviso that the new head of hockey operations would have the ultimate say on that. But let’s be real. The candidate with the best chance of winning the job is likely to be the one who shares ownership’s view on whether to retool or rebuild. That’s how these things work.

For example, some candidates who interviewed for the Pittsburgh Penguins general manager job three years ago didn’t hide the fact that they felt that the Pens’ aging roster needed a full teardown. That’s not what ownership wanted to hear. It wanted to hear about the team remaining competitive in the short term around Sidney Crosby, Evgeni Malkin and Erik Karlsson while also getting younger over time and restocking the cupboard. The guy who said he could deliver on that was Kyle Dubas. And well, he has, which has been rather impressive.

The reason I bring this up is that I know there were some potential candidates for Leafs GM keenly watching Tuesday to hear what Pelley would say on that subject. And I know some candidates may not be as interested in the job if they don’t get full autonomy to do a rebuild instead — because they believe the Leafs have so little coming in the pipeline that they need to reset things more fully than MLSE ownership may be willing to accept.

It’s something to consider as Pelley and the search firm he’s bringing in whittle down their list of candidates.

This is where the chicken-and-the-egg situation gets interesting. The new head of hockey operations will want to know how Auston Matthews feels about his future in Toronto before fully setting a new course for the organization. But in turn, the Leafs captain and his agent, Judd Moldaver, will want to know what course is being charted by management before deciding what they want. That’s a delicate balance. Who blinks first?

Matthews alone could decide the rebuild-versus-retool path, depending on his course of action.

Still, even with that complication and with how things look at the moment, it’s a job that is very coveted across the league.

So you’re going to hear about all kinds of names over the coming weeks.

One you won’t hear is Jim Nill. It was interesting timing indeed that the Dallas Stars announced his two-year contract extension on Tuesday, a day after Leafs GM Brad Treliving was fired. My understanding is that Nill and the Stars had agreed to the deal a few weeks ago but hadn’t announced it. Hearing Nill’s name bandied about by Toronto media Tuesday morning was probably enough incentive for the Stars to put an end to that. Nill’s current deal was expiring after this season. So it was pretty darn important for the Stars to get done for the three-time GM of the Year extended — and, well, scratch his name off Toronto’s list.

And what about Doug Armstrong, the outgoing Canadian Olympic GM? He’s atop most lists of candidates, and his body of work certainly suggests he should be. Armstrong’s headed to the Hockey Hall of Fame one day. But he’s not a free agent. There seems to be some confusion over that because he’s stepping down as GM on July 1, but he signed a three-year extension to be president of hockey operations and help guide new GM Alex Steen in St. Louis.

That’s not to say the Leafs shouldn’t covet Armstrong, and in fact, they’d be crazy not to reach out to the Blues and ask permission to speak with him. But it comes down to Blues owner Tom Stillman deciding whether or not he would entertain letting Armstrong talk to the Leafs. I’m not sure why he would, but if Stillman felt Armstrong really wanted the Leafs job, I suppose you never know.

Then there’s Michael Gillis, the former president of hockey operations and GM of the Vancouver Canucks. When you hear some of the things Pelley had to say Tuesday about “data-centric” candidates and A.I. and a modern approach to running an NHL organization, that screamed Gillis. I remember doing an interview with Gillis for The Athletic back in March 2019 about his world travels and the things he was studying to further understand sports and athletes and science. It was fascinating.

I don’t know if it’s been too long away from running a team for Gillis, but hearing Pelley talk on Tuesday, it’s like he and Gillis share a brain. I would be surprised if they didn’t talk during this search process.

When all is said and done, I do think it’s likely we are looking at multiple hires here: a veteran hand with an up-and-comer, that kind of thing.

Not replacing Brendan Shanahan last year as president was probably a mistake. It left Treliving with too much on his plate, and it forced Pelley to spend too many hours in hockey ops. He said himself Tuesday that he’s not interested in doing that again, as far as living in the weeds of the hockey department full-time.

These are massive hires for an organization that has cratered in just two years. The retool might be wishful thinking. I think a rebuild is more realistic. But Dubas proved me wrong in Pittsburgh, so I suppose the new Leafs GM could prove me wrong, as well.