It follows a campaign by Croydon mum Catriona Ogilvy which has been backed by over 350,000 people.
Current law states maternity and paternity leave begins the day after birth even if a baby is born premature.
Treasury minister Kemi Badenoch said the government would pay the extra leave, rather than businesses.
Mrs Ogilvy – who spent time in a neonatal ward after her son, Samuel, was born 10 weeks early – has petitioned to extend parental leave following premature birth since 2015.
Her campaigning has seen the Mayor of London, Sony Music and a number of London councils adopt policies to give extra leave to staff who have babies born early.
It is expected that Chancellor Rishi Sunak will outline plans for Neonatal Pay and Leave on Wednesday to allow new mothers and fathers to claim statutory paid leave for every week their child is in neonatal care, up to a maximum of 12 weeks.
Mrs Badenoch, the Minister for Equalities, told the Sunday Times the move would be “historic”.
“This will be in addition to the usual maternity and paternity leave, and finally give parents the time, the resources and the space to handle these difficult circumstances,” she said.