It would be an extraordinary rise to fame for someone who has never held a cabinet post and has less than 13 years experience as a councillor.
Brew, a councillor for Northfield, was unavailable for comment this afternoon, but his supporters were keen to talk about the leadership bid.
Most members of the 49-strong Tory group have been approached by Brew or his campaign managers during the past week.
One senior Conservative councillor said Brew had a good chance of toppling Whitby because he was seen as a moderate who would win the support of the Liberal Democrats, who have been running Birmingham in coalition with the Tories since June 2004.
He said the challenge was the culmination of a number of events over the past two years, starting with announcements about the £193 million Library of Birmingham which is to be built in Centenary Square. Backbenchers were angry at being "kept in the dark" over such an important decision.
Further examples of Coun Whitby's apparent failure to keep grassroots Tories informed followed with proposals for an £80 million Olympic swimming pool and then, just before Christmas last year, the disclosure that the council was to bring back the municipal bank at a cost of £200 million.
The bank issue prompted a dozen angry Tory councillors, including Brew, to write to the Post complaining that such a venture would be a waste of money.
The tipping point, according to backbenchers who have spoken to the Post, was the decision to bankroll Warwickshire County Cricket Club's £32 million ground improvement scheme with a £20 million council loan. The deal, to which Whitby gave his personal backing, began to unravel when the planning committee refused to grant approval and a scrutiny committee ordered the cabinet to reconsider the loan.
Pressure on the council leader grew when an analysis of the club's finances by Deloitte raised serious doubts about the accuracy of the business case.
Whitby was supposed to attend the scrutiny committee to answer questions about the loan, but failed to turn up.
His excuse, that he had to entertain the Jamaican High Commissioner, looked somewhat thin when he was spotted heading off with his wife to London for a performance of the Birmingham Royal Ballet while the committee was still sitting. That prompted John Alden, like Whitby a Harborne Tory councillor, to complain that scrutiny was being ignored and treated disgracefully.
A stormy Conservative group meeting saw the rebels becoming increasingly confident, demanding the establishment of a 1922 Committee to improve backbench links with the leadership. Whitby was told in no uncertain terms that he would have to mend his ways by becoming more inclusive.
One Tory backbencher said today: "Whitby has done little to address our concerns. There was a promise that he would change, but he is carrying on as before.
"He clearly thinks he is untouchable, but this is a serious bid to topple him.
"It's too soon to say what might happen, but it is entirely possible that Coun Brew could do it."
One of the most senior Tory councillors outside of the cabinet said: "The £20 million loan to the cricket club really annoyed people and the council leader's failure to attend a scrutiny committee made matters even worse.
"We were all told when the cabinet system came into existence that scrutiny committees would be able to hold cabinet members to account, but we are simply being ignored by the council leader who presumably feels he is free to do whatever he wants."
Coun Brew, a chartered accountant who built up his own business, first clashed swords with Coun Whitby in May 2007 upon becoming Lord Mayor.
A furious row broke out behind the scenes over Coun Whitby's successful attempt to change the council constitution to state that the Lord Mayor must not take a lead or civic role in matters that are in the interests of the leader of the council or any other cabinet member.
Labour, and many Tories privately, claimed the change was designed to allow the council leader to overshadow the Lord Mayor at civic and council functions including royal visits.
This will be the first leadership challenge Coun Whitby has faced since becoming council leader.
A revolt this time last year, not led by Coun Brew, fizzled out when a handful of backbenchers withdrew their support and switched sides to back Whitby at the last mintue.