Notley said Wednesday that Merwan Saher's original investigation looked only at Redford's team, and other ministers who worked with her remain in Premier Jim Prentice's cabinet.
She said even though Redford has left government and Prentice has promised new rules on behaviour, the issue is not moot.
"If other people who are actually still in there (are) engaged in behaviour that may well itself warrant criminal investigation, then, in my books, that's not moot," Notley said at a legislature news conference.
"Those aren't the people that I want running my budget or my government."
She said she has sent a letter to Saher asking him to investigate further.
She's sent a separate letter to Prentice asking him to join her on the request. Prentice, in a written response, declined.
"The very first cabinet decision that was made when I became premier was to sell the government air fleet, and that process is currently underway," he said.
"I have full confidence in the office of the auditor general to determine when and where an investigation is appropriate."
More than half the members in Prentice's current cabinet served in Redford's cabinet.
Redford quit as premier in March ahead of a caucus and party revolt over reports of exorbitant spending on herself and her inner circle.
In August, Saher said his investigation found Redford and others had abused public trust by using government aircraft for personal reasons or to attend partisan political events.
He said Redford at times used the planes to fly her daughter and her daughter's friends around. On two occasions her daughter flew solo.
More damning was evidence that Redford's team added phoney passengers to flight lists to give the impression the plane was booked, which allowed Redford and her team to fly by themselves.
Just as Saher's report came out, Redford quit as a member of the legislature for Calgary-Elbow.
She has never commented on the case publicly except to say "mistakes were made."
Saher noted that both Redford and Farouk Adatia, who was her chief of staff at the time, had no knowledge of the block booking.
But he also said in his report that "based on our interviews, the idea for restricted access to the aircraft came from the (premier's) office."
Earlier this week, the CBC reported that an August internal government analysis based on Saher's report determined that the allegations of fake block booking could, if proven, lead to criminal charges of fraud, breach of trust, forgery and uttering a forged document.
The government then sent the information to the RCMP for review.
Last week, the Mounties announced that the review has become a criminal investigation, but they declined to say anything more.
Jeff Wilson, a critic for the Opposition Wildrose party, agreed that the auditor general needs to investigate further.
Wilson said Albertans need assurances that current cabinet ministers or government caucus members have not been engaging in behaviour that would warrant a criminal investigation.
"There appears to be enough evidence to warrant a broader investigation from the auditor general," he said in an interview.
"Albertans are increasingly disappointed with this type of behaviour from their elected officials and frankly deserve better."
Liberal Leader Raj Sherman has said Prentice needs to remove anyone in caucus if they are under RCMP investigation.
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