Currently parents who home-school children can choose whether to register them with the local authority, which can only carry out informal monitoring.
The Association of Directors of Children's Services (ADCS) has said tougher regulation is needed due to an increase in the number of children being home-schooled, which is making it harder for councils to ensure children are receiving a good education.
Between January 2016 and October last year the number of home-schooled children increased by 21 per cent to around 45,000 according to ADCS research, although the government believes the true figure could be even higher.
The Department for Education (DfE) has now called for views on whether the current regulations need to change, stressing that it is yet to take a view on whether an overhaul is required.
This follows a commitment made in November to review guidance for councils in relation to home-schooling.
In consultation documents published this week the government emphasises that it wants to safeguard parents' right to home-school their children.
However, it adds that it is keen to hear more views on reported difficulties in ensuring children are receiving a good education.
It also wants to gather views on the effectiveness of the present system of voluntary registration and councils' informal oversight of the quality of education.
"Government intends to safeguard the primary duty of parents to lead their children's education, including the provision of home education. It does not intend that the state should supplant this parental role," the consultation document states.
It adds: "This document does not put forward any specific government proposals for change."
The rise in home-schooling detailed by the ADCS is also cited by the government as a factor in the review.
Ministers are also interested to know how parents involved in home schooling can be better supported, although the consultation document stresses that families will continue to "take financial responsibility" for their children's education.
The document adds that current home-schooling laws "were designed for a different age", as they originate from the Education Act 1944.
"This government's vision is to ensure that all children and young people receive world-class education in a safe environment so that they all have the opportunity to succeed and reach their potential, regardless of background," the document adds.
"The [DfE] believes that home education is often good and that it is a valid way of realising these ambitions for children. However, there is no assurance that this is always the case."
Other home-schooling "problems" the government wants to look at include lack of data on how many children are being home-schooled.
Another is so-called "off rolling" where schools allegedly persuade parents of challenging children to take up home-schooling as an alternative to exclusion.
"Many local authorities have said that this practice of 'off-rolling' is increasing, although by its very nature this is hard to prove," the consultation document states.
"This is potentially highly damaging to a child's education."
Also of concern are council reports that home-schooled children are at an increased risk of radicalisation "because of both the type of education they are receiving and their reduced contact with professional services".
The danger of radicalisation has also been raised in a previous government consultation on illegal schools.
The Local Government Association's children and young people board vice chairman Roy Perry has welcomed the government's review of home-schooling.
"Councils fully support the rights of parents to educate their children in the best way that they see fit, and the vast majority of parents who home educate their children do a fantastic job, and work well with their local council to make sure that a good education is being provided," he said.
"But for the minority of children where this is not the case, councils need the powers and appropriate funding to enter homes or other premises to check a child's schooling, and make sure they aren't being taught in unsuitable or dangerous environments.
"Placing a legal duty on parents to register home-schooled children with their local authority would also help councils to monitor how children are being educated and prevent them from disappearing from the oversight of services designed to keep them safe."