Nottingham City Council will decide then which centres will be taken over by community groups.
The centres proposed for closure, unless another provider can be found, are Aspley (Amesbury Circus), Aspley (Minver Crescent), Bilborough, Bulwell and Sneinton.
Concerns have been raised by community leaders that the cuts are in some of the most deprived areas of the city and will cause major problems for families and children in the future.
The centres provide a range of services including midwifery, antenatal and post-natal clinics as well as early help for vulnerable parents including those who have children with disabilities.
The council says eight of the 17 children’s centres in Nottingham are operated by schools, which are not affected by the proposals.
The council were looking for new organisations, schools, or community groups to deliver services in children’s centres, including those earmarked for closure.
A consultation was launched and is now concluded.
The Labour-run authority, which has debts of £900 million, has planned to make £38 million of savings over the next four years.
Some of these savings will come from closing five of its nine children’s centres.
At a meeting of the children and young people scrutiny committee on June 9, councillors asked senior management about the proposals on the table.
Alison Barr, director of children’s integrated services, said: “The decision around how the buildings will be run in the future and which groups will run them will be made in July.
“It is positive there were services across the city that wanted to run services for the community from these buildings.”
However, leases will be weighted on whether the organisations can prove they have ‘financial sustainability’.
So far, eight organisations have shown an expression of interest of taking over the running of the buildings.
Coun Georgia Power (Lab), ward councillor for Bestwood, said: “Not everyone would have read or known about the consultation so there is missed opportunities.
“What I don’t want to happen is groups have missed out.
"Nothing has come to me as a local councillor and I thought you would want to get it as far and wide as possible rather than hidden in a consultation document.”
Coun Carole McCulloch (Lab), ward councillor for Aspley, added: “These buildings have been in the community for time and it is going to be a massive thing to have them lost.
“It feels like we are chopping our foot off and I am hopping.
"We really need to go as far as we can so that local communities deliver services in there – it is where they have been brought up.”
Coun Cheryl Barnard (Lab), portfolio holder for children and young people, who represents Bulwell Forest on the council, explained some of the concerns raised by families.
She said: “There was a lot of concerns on buildings that had childcare provision in them and a lot of concern from parents about how they will receive services.
“There were also concerns about isolation and mental health and support for parents.”
The centres proposed to remain open are Broxtowe, Hyson Green, Meadows and Southglade (Bestwood/Top Valley).
The proposals would introduce a new citywide early help offer through support out in the community, including face-to-face sessions delivered both within the remaining children’s centres and also in venues across the city.
The saved centres will also work with the most vulnerable families in the city.
However, this also raised concerns with other councillors.
Coun Power asked: “What do we do if demand outstrips supply?”
And Coun McCulloch added:
“They don’t want someone in a suit knocking on their door.
"They go to children’s centres because they want to go to children’s centres.”