Currently workers need to earn at least £118 a week to receive statutory sick pay, the equivalent of at least 14 hours on the minimum wage.
The government has launched a new consultation on whether to extend eligibility to those earning below this threshold. There could also be more help for those returning to work after sick leave.
Health Secretary Matt Hancock said: "We need to remove the barriers that stop people with disabilities or health conditions from reaching their full potential - these steps will help us achieve that."
Gig economy companies such as Deliveroo employ staff on short term contracts that do not offer holiday or sick pay. It is unclear if the plans would benefit "gig" workers on freelance or short-term contracts, but the Department for Work and Pensions said the consultation did not seek to "undermine the flexibility in the UK labour market".
Around 1.1 million people in the UK are considered gig economy workers, receiving little or no holiday or sick pay.