The local authority has been criticised for plans to withdraw funding from nine of its 15 children's centres. Fifty jobs are also expected to be lost.
Councillors were due to meet at a cabinet meeting on Monday to discuss proposals to restructure children's centres round six hubs.
The council is proposing to cut £6.95m from its children's services budget.
However, the council denies that it is closing centres and says it is planning a 16th children's centre at Baron's Court library, which would be run with local community groups.
Conservative Councillor Helen Binmore said, 'We want to avoid having to close any centres and our initial discussions with other local organisations suggest that, by working creatively together, we will be able to find significant savings from sharing running costs and reviewing the services on offer.'
Council documents state that it currently expects to lose £4.2m in external grants in the spending review for early intervention services, including a significant part of the current funding for phase three children's centres.
The papers say, 'It is therefore highly unlikely that we could continue to fund all current children's centres and targeted provision for vulnerable families while meeting these savings targets,' and that cutting targeted support for the most vulnerable families would 'almost certainly' lead to a rise in looked-after children.
'It must be a priority to support children and families who are vulnerable and to ensure the provision of targeted services.'
The council aims to contract out provision to schools or private sector providers, while maintaining some provision at most centres.
It said that some centres are already attached to schools and that the council expects that many would want to continue running provision, such as out-of-school clubs.