Mr Kean will throw his hat into the ring for the deputy's job alongside Transport Minister David Elliott.
"I'll be putting my name forward and that'll be up to my colleagues to decide whether or not they'd like me to fill this role," Mr Kean told reporters on Monday.
Mr Ayres resigned from cabinet and as deputy leader after a draft review found he had not remained at arm's length from the appointment of Mr Barilaro to a New York trade job, and may have breached the ministerial code of conduct.
His ministerial portfolios have been redistributed and the party will on Tuesday vote on his replacement as deputy.
Mr Elliott, who takes over the Western Sydney portfolio from Mr Ayres, announced last week he would contest the deputy leadership.
Mr Kean leads the centrist "moderate" faction of the party while Mr Elliott is known for being a conservative. The pair have a history of conflict.
Mr Elliott told News Corp he would withdraw from the contest if Mr Kean also stepped aside for a woman to fill the role.
Ten of the 33 Liberal members in the legislative assembly are women.
Eleni Petinos was also dumped from the ministry last week after bullying allegations emerged from her office, while Gabrielle Upton has already said she will not contest March 2023's state election.
Only one remaining Liberal woman eligible for the deputy leadership, first term member for Goulburn Wendy Tuckerman, is a minister. She has not confirmed an intention to run.
Meanwhile, Premier Dominic Perrottet, who is dealing with the toxic fallout from the Barilaro job controversy, has admitted he spoke with Mr Elliott about potential jobs the current transport minister could do after retiring from politics, but denies promising a future role.
"The allegations in relation to the creation of a role that I would give to somebody outside politics is completely false and offensive," Mr Perrottet told Sydney radio 2GB on Monday.
It is the first time the under-pressure premier has directly responded to reports he offered to create an overseas trade job for Mr Elliott or make him the agent-general in London when he was putting his cabinet together in December.
"David Elliott was never promised a job outside of politics," he said. "That is deeply offensive and wrong."
A Nine News report said the premier talked about post-politics jobs with Mr Elliott after the member for Baulkham Hills flagged his interest in running for a federal seat in the May election.
"From time to time discussions will be had in relation to when someone retires, what they would like to do," Mr Perrottet said.
He admitted other roles were discussed and did not deny the job of NSW governor was raised.
"I have colleagues speak to me from time to time about what roles they could play in the NSW parliament to continue to serve the people of NSW," he said.
"These are natural conversations that a premier or a prime minister has with their team."
Labor wants the parliamentary inquiry examining the appointment of Mr Barilaro to the coveted US job to be expanded to include other postings, and says it will abolish overseas senior trade roles if it wins next year's election.
