Sheffield Council plans to replace children's centres with new family centres as part of a city-wide change to the way it supports young people.
The authority wants to get rid of the 16 existing children's centres in Sheffield.
Instead, support would come from seven new family centres - which would cover those aged up to 19, or 25 if they have a disability - and a range of outreach services.
Children's centres currently work with children aged up to five, and offer preparation for parenthood groups, health clinics, toddler groups, training for work, information and advice.
The council believes the new model would be more flexible and would better meet families' needs.
But concerns have been raised that outlying areas of the city would suffer as a result of the loss of the children's centres.
As the vice chairman of governors at Ecclesfield School, Mike Levery is based in one such area.
He said: "Outlying places like Stocksbridge, High Green and Mosborough will not have any children's centres any more. They are going to do it through outreach.
"But if they don't have a children's centre there, how are they going to get to north Sheffield's needy families?
"Looking at the models they have put up, there's nothing beyond Parson Cross and Ecclesfield. It talks about link centres but they haven't said what they are."
Mr Levery suggested that the reduction in the number of centres would put strain on existing services, making it more difficult for people to access support.
"The inference is that if they need the services they can go to the nearest centre to access them - but it might be a long way, and people just won't do it," he said.
And speaking in terms of his own school, Mr Levery said the benefit of the existing centres was becoming clear.
"We have had some pretty poor cohorts in the past few years at Ecclesfield School, but we can now see that the children's centres have had some impact, because we are getting much better cohorts. We are expecting some good results.
"The children's centres started in 2004. The children are now hitting secondary school and you can see the difference."
The consultation is open until January 31. Drop-in events took place before Christmas, and more will be held in the new year.
The council's head of service for children's centres Nicola Shearstone said the new model would be better for families.
She said the idea was to build partnerships with existing services all over Sheffield, focusing on early support in order to prevent problems.
The new model would try to link people with relevant services through outreach work, and engage people who otherwise wouldn't visit a children's centre.
And the idea behind family hubs, said Mrs Shearstone, was to offer support to the whole family rather than have a specific focus on early years.
She added: "The difficulty is that people see children's centres as a building. But they are more about an area.
"When we are looking at the seven communities for family hubs, we are splitting the whole city into seven areas. Each will have one site and we will then use a range of buildings across the area.
"Even with the number of centres we have, some families don't feel they can get to the building to access services.
"We are trying to improve that by using more opportunities and buildings."
The family hubs would cover the following areas: Parson Cross/Ecclesfield; Shiregreen/Burngreave; Arbourthorne/Manor/Darnall; Mosborough/Handsworth; Greenhill/Gleadless Valley; and Rivelin to Sheaf and Hillsborough/Upper Don.
Mrs Shearston said this model would allow the council to be more flexible when catering services to the needs of particular areas.
She said the whole service would still be inspected by Ofsted, and insisted the changes were not about saving money.
"This is more about looking at the focus of our services. It's not about cost saving."
Mrs Shearstone said she did not envisage any staffing changes.
Once the consultation closes, feedback will be analyses and a final proposal will come back to the council towards the end of spring.
To take part in the consultation, visit www.sheffield.gov.uk or call 0114 2813758.
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