Chancellor Rishi Sunak is reportedly considering the moves after already extending grants to employers with workers on furlough until the end of October.
But although the holiday will stay open, Westminster sources suggest the terms could restrict the number of borrowers who can apply.
Mortgage holidays and the eviction ban are due to end in June.
If the scheme is extended, lenders want to put borrowers into one of three groups – those that should return to normal payments, borrowers who need short-term help and those who are unlikely to repay their loans and need debt advice.
So far, mortgage lenders have deferred monthly payments for 1.7 million borrowers, including tens of thousands of landlords.
The average mortgage payment for those struggling to pay their bills because of the impact of coronavirus is £755 – but lenders warn the holiday could add an extra £2,769 in interest over the loan term.
Lenders have agreed to the arrangements without putting a black mark for the missed payments on a borrower’s credit rating.
Landlords are meant to pass the saving on to tenants. Renters must agree terms to repay the rent once the pandemic fades.
Landlords face higher monthly mortgage payments after the holiday as balances are recalculated over the existing term to account for the missed amounts.
Meanwhile Housing Minister Christopher Pincher has confirmed the repeal of Section 21 no-fault eviction rules once the coronavirus emergency is over.
In a reply to a written question in the Commons from Labour’s Shadow Housing Minister Thangam Debbonaire asking when the government intended to implement the policy.
“We will respond fully to the consultation on tenancy reform in due course, when the urgent concerns of this emergency have passed,” said the minister.