Andrew Scheer's resignation is barely a day old, but pundits, as well as party insiders, are already looking at what's next — or rather, who.

For some, former federal Conservative MP Rona Ambrose tops the list.

Alberta Premier Jason Kenney told Postmedia that she'd be a brilliant choice for leader.

And on Twitter, former Saskatchewan premier Brad Wall said although he's flattered to be called to run, he's not interested but hopes Ambrose is.

Thank you to those of you who have DM’d and tweeted me about running for the <a href="https://twitter.com/CPC_HQ?ref_src=twsrc%5Etfw">@CPC_HQ</a> leadership. I am honoured that you feel I could contribute at that level but I will not be a candidate for the leadership. I am hopeful however that <a href="https://twitter.com/RonaAmbrose?ref_src=twsrc%5Etfw">@RonaAmbrose</a> decides to be a candidate. —@BradWall306

She was the interim Conservative leader after Stephen Harper stepped down following the 2015 loss to the Liberals. She left politics in 2017.

Ambrose has since served on Prime Minister Justin Trudeau's NAFTA advisory panel and has worked for organizations advancing girl and women's rights.

But so far with the public calling on Ambrose to run for the leadership, she hasn't made any statements — and declined CBC's request for comment.

Mount Royal University political scientist Lori Williams agrees with the whispers, she says Ambrose would be a great candidate. But she says there is a lot to consider.

"She hasn't said no," Williams said. "Presumably she's being courted and she's thinking about it. It's a very big move to make and we saw what happened to Andrew Scheer. She knows she'll be walking into a bit of a lion's den here."

What kind of conservative?

One challenge Williams sees is keeping the Conservatives united. While she adds Ambrose might have the right leadership style, things could just as easily fall apart.

"I think her record of being a bit more of a conciliatory figure, somebody who reaches across divisions, that I think could be one of the things that equips her well to deal with some of the challenges within the party," Williams said. "But, you know, some people are very angry and they aren't interested in conciliation."

In Banff on Thursday, former federal politician Stockwell Day said there's nothing wrong with a socially conservative leader.

"I think most Canadians aren't bothered by that as long as they don't feel that somebody's personal views are being imposed on them or legislated," Day said. "But there are people who are not satisfied with that in our country today. There are people who are not satisfied with somebody being allowed to be in office who has certain views."

Calgary Confederation MP Len Webber says the next leader must be willing to march in Pride parades and advocate for women's rights.

"I certainly am of the belief that it should be someone more progressive this time around," he told reporters in Ottawa, before heading into question period.

Should candidate be from the West?

Political strategist Zain Velji appeared as part of CBC Calgary's political panel Thursday night. He has worked on several campaigns, most recently with the NDP.

"Does it even help to have a western leader?" he asked host Andrew Brown. "Or do we go out East."

He suggested someone like a Peter MacKay or similar. The Conservatives already have the vote in Alberta locked down, he said, and they need to make gains in Atlantic Canada, Quebec and Ontario.

Jason Markusoff, also on the TV panel, said to watch out for a regional faction, over and above the progressive versus social conservative debate.

I do think we need to be a bit brave and bold - Tim Powers, vice-president Summa Strategies

"There's western-eastern, energy versus environment and climate change," Markusoff said. "There could be a Rona Ambrose type who tries to bridge that. But I would imagine given the sense of rage and frustration with Trudeau in Alberta and Saskatchewan, you're going to see a Prairie-first type candidate."

On the Calgary Eyeopener, Tim Powers, vice-chairman of Summa Strategies, told host Rob Brown it's more about the leader, not geography.

"I do think we need to be a bit brave and bold," Powers said. "I'm not restricting where that person should come from, but whoever becomes the leader I think has to be comfortable in all parts of Canada and with all sorts of diverse Canadians and conservatives."

Powers hopes Ambrose or MacKay throws their hat in the ring.

New leader inheriting a challenge

Williams agrees, saying now more than ever the Conservatives need a skilled leader, with parliamentary experience, to throw the Liberals off their game.

"It's just going to be a challenge, both in terms of the party and in terms of the country, to try to represent and make those who are dissatisfied with the current state of affairs to make them feel heard," Williams said.

"A skilled leader with a good vision could be a real threat to the Trudeau minority government."