The Queen's Speech said the Government would work to "remove barriers to flexible working" with ministers now set to begin consulting with business leaders.
Parents of children aged 16 and under, parents of disabled children aged up to 18 and carers of certain adults currently have the right to request flexible working hours from their employers.
A statement on the Downing Street website said: "Extending the right to request flexible working to all will ensure that individuals within the wider caring structure, e.g. grandparents and neighbours will be able to take a more active role in caring and manage their work and family lives effectively. This extension will also help to remove the stigma attached to flexible working requests at the moment."
The new Government said that flexible working hours will bring benefits for businesses as it will increase staff morale and productivity, as well as improving staff retention rates and creating a wider pool of skills within the workforce.
It also said the benefits for families and society generally would be massive, adding: "We want to take the time to consult fully with business and families, to identify the best way to make this extension. Rushing legislation on this issue would not allow full consultation."
But David Frost, director general of the British Chamber of Commerce, claimed businesses were already willing to make flexible arrangements, adding: "We do, however, have serious concerns over any additional Government regulation in this area, whether this occurs now or in the medium-term."
TUC general secretary, Brendan Barber urged the Government to enact reform to ensure greater flexibility as soon as possible.
He said it would bring "positive change" to the country.