Senior Labour insiders say Councillor Sadie Docherty, who represents Linn, is now tipped to take the top job.
It had been thought Stephen Curran, councillor for Newlands and Auldburn councillor, and Paul Rooney, Garscadden and Scoutstounhill member, were the top contenders for the role.
Former Provost Liz Cameron, who served between 2003 and 2007, was also a contender.
But Mrs Docherty is favourite for the post, which would see her in the spotlight during the Commonwealth Games in 2014.
Closing dates for nominations for Lord Provost close today and the Labour councillors will make their choice tomorrow.
If elected, Mrs Docherty will be only the fourth woman to become the city's Lord Provost, after Liz Cameron (2003-07), Susan Baird (1988-92) and Dame Jean Roberts (1960-63)
A senior council insider said: "Sadie is very well respected across the council.
"She is seen in the chamber as a champion for women and the education of children."
She was elected to the city council to represent the Linn ward in 2007.
She was born and brought up in Castlemilk and has risen rapidly within the council during those five years and is currently the chairwoman of the Community Planning Partnership.
The councillor, who has a grown up son and daughter, lives in the Linn area with husband Willie, a former managing director of City Building.
Mrs Docherty was previously a community housing manager with GHA, a youth leader and has been a member of the Children's Panel.