Keith Brownsey, a political science professor at Calgary's Mount Royal University, said a few names keep popping up.
Among them: Alberta Finance Minister Doug Horner, former Edmonton mayor Stephen Mandel, past federal cabinet minister Jim Prentice and former provincial treasurer Jim Dinning, who lost a leadership bid for the party in 2006.
Brownsey said Mandel and Dinning may be the best choices for the Tories, but they may not want to run a party that's sinking after four decades in power.
"Really, this is a party in free fall. It's a party that has tossed its last four leaders," he said.
"Who'd want to take that job?"
Redford resigned on Wednesday after weeks of caucus unrest and criticism over her leadership style and questionable expenses.
Political scientist Doreen Barrie at the University of Calgary said she's heard the same names being tossed around.
She added that Labour Minister Thomas Lukaszuk may have the most public profile of the sitting caucus members and could also throw his hat in the ring.
Len Webber, the first caucus member to cross the floor and publicly question Redford's leadership, has indicated he wants to run federally but could change with the premier's chair open, said Barrie.
But she said no one currently in the legislature stands out as a prime candidate and she believes the party's new leader will come from the outside.
Politics in the province have been a "snooze-fest" in the past, said Barrie, but the recent drama is making it exciting.
She said even with a new leader, the Tories will have to stay on their toes because the Wildrose is proving to be a strong Opposition.
"I think it's a mistake for them to think their troubles are over. They're just beginning."
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