Redford dodged questions from reporters about her leadership during arrival at the meeting, in which party directors are expected to talk about the controversy surrounding her over the past few weeks.
Many of the complaints about the premier have stemmed from the costs surrounding her $45,000 South Africa trip to attend Nelson Mandela's funeral.
Nova Scotia Premier Stephen McNeil spent less than $1,000 to make the same trip, and Redford has also been under pressure for her use of Alberta government aircraft on several other occasions.
Although she did repay the money this week — after weeks of refusing to do so — it's expected the trip will be one of the concerns highlighted by party executives at today's meeting, said PC Party president Jim McCormick.
It had been rumoured several of her MLAs were ready to leave caucus over the issue, although only one actually did.
Len Webber abandoned the party to sit as an independent Thursday after, he says, he received continued angry feedback from his constituents in Calgary-Foothills over Redford's "abuse of government aircraft and abuse of our taxpaying dollars."
"I cannot put up with it for any longer," Webber said.
The president of a PC riding association in Edmonton called for Redford to resign Friday, saying her leadership put the party's chances of winning the next election at risk.
"Her leadership has slammed the door from all the people that got the party to where it is," said Steve Robson with the Edmonton Beverly Clareview Progressive Conservative constituency association. "I don't like what I see going forward for the PCs' chance with Alison as the leader. So the longer that they stick with her, the tougher it's going to be at the next election for them to come out victorious."
The party does not have any constitutional mechanism to remove Redford from her position if it wished to do so.
There was a leadership review but she passed that test with a 77 per cent approval rating.