The controversial proposal is part of major shake-up of provision, as Cornwall County Council looks to reorganise children's services. Among measures outlined in the council's One Vision strategic document is to "introduce means-tested charging for a range of family support services".
Although the document does not specify which services would incur charges or how means-testing could work, family support typically includes provision such as health visiting, parenting courses, or short breaks for disabled children.
However, Sally Hawken, Cornwall's lead member for children's services said that there are no immediate plans in place to bring in charges for family support.
"At the time of its (One Vision) writing it was agreed that there should be something which allowed for the possibility of looking at charging for things at some point in terms of reducing resource and rising demand," she said.
"We can't between now and 2020 ever possibly rule it out but it's absolutely not on the table. It's not under active consideration in any shape or form."
Cornwall Council is not the first to consider charging families for support. In 2013 Worcestershire County Council put forward proposals where parents could be forced to pay as much as £900 a month if their children were taken into care.
The proposals have been criticised by union Unite, which has warned that if charging is introduced it will likely involve families paying for health checks from health visitors.
"We are at a crossroads in Cornwall as to how we look after and care for babies and young children," said Unite regional officer Deborah Hopkins.
"The prospect of means testing for such children's services, including visits by health visitors, will be an anathema to the vast majority of Cornish people.
"Even the One Vision framework admits that child poverty is ‘a persistent issue in some areas'.
"One of the founding principles of the NHS in 1948 is that health services should be free at the point of delivery for all those in need - the proposals in the One Vision document are throwing these principles out the window."
She added: "Cornwall, so reliant on the seasonal tourist trade, is reportedly the second poorest region in northern Europe, so I am not sure where councillors would expect hard-pressed parents to find the cash to pay for a visit from a health visitor."
Ethal Rodrigues, Unite's lead professional officer for the South West, says that Cornwall's situation is "not unique".
"Other cash-strapped authorities across England are eroding the provision of children's services, as they grapple with severe Tory cuts to local government budgets," she said.
"The problem is compounded by the dramatic slump in the number of health visitors since the health visitor implementation plan ended in 2015, which we are campaigning to reverse."
Plans outlined in the One Vision document to reorganise children's services in Cornwall will go before members of the council's cabinet tomorrow evening (7 November).
Councillors are being recommended to back the formation of a council-run "Integrated Children's Services Directorate" (ICSD), bringing together education, early years, early help, children's social care and children's health, including health visiting services. If approved the plans could be implemented from December.
This is the preferred option over an alternative delivery model, involving a council-owned company running an integrated service. However, cabinet members are also being asked to continue to "consider the benefits" of this model.
In October 2017 the council received £1.9m from the in Department for Education's Social Care Innovation Programme to explore alternative ways of delivering children's services.
Unite has urged the council to ensure children's services remains in-house.
"We need to have the widest public consultation possible and keep our children's services in the hands of the taxpaying public and not outsourced to a profit hungry company," added Hopkins.
A report on the proposals said that the integrated children's service will save money for the local authority, help tackle rising demand, and better co-ordinate support for families as well as help the service boost its Ofsted rating.
"The proposal for an ICSD is aimed at creating an environment and the means where services for children currently delivered and commissioned by the council can go from an Ofsted rating of 'good' to 'outstanding' in the challenging context of rising demand and reduced resources, increased statutory duties and raised standards," states the document.
Cornwall Council was criticised earlier this month for housing a vulnerable homeless teenager in a tent. A report by the Local Government and Social Care Ombudsman said the 17-year-old's ordeal left him emaciated and resulted in him being detained in a psychiatric hospital for nearly a year.