According to the Times, Mr Johnson will support Mr Sunak in a cabinet split over an extension to the £20 per week uplift for six months rather than a year.
The Chancellor is reportedly locked in a battle with Work and Pensions Secretary Thérèse Coffey, over when to remove the uplift.
It was introduced in March 2020, in response to the coronavirus pandemic.
Mr Sunak said at the time: “To strengthen the safety net, I’m increasing today the Universal Credit standard allowance, for the next 12 months, by £1,000 a year.
“For the next twelve months, I’m increasing the Working Tax Credit basic element by the same amount as well.”
The Government has said the cost of the measure comes in at £6billion per year.
A new report from the Work & Pensions Committee was published today, which recommends that if the Chancellor cannot yet commit to making the £20 uplift to Universal Credit permanent, he should at the very least extend it for a further 12 months.
Responding to the report, Iain Porter, Policy & Partnerships Manager at the Joseph Rowntree Foundation who gave evidence to the inquiry, said: “We fully support the committee in calling for the Government to commit to keeping the £20 uplift to Universal Credit for at least a year.
“A short term extension of anything less than 12 months is not the answer as it would cut support for the poorest in our society just as unemployment is expected to peak later this year and remain high for some time.
“There is a widespread consensus that cutting benefits now would be a terrible mistake as it will have devastating consequences for people’s health and ability to recover from this economic crisis, as well as for our economy and local communities that the Government has committed to level up.
“Millions of families have experienced job losses and income shocks over the past year and there is sadly still more to come.
“If the Government is serious about supporting families through this crisis, it cannot create more uncertainty and pressure for them, but should extend this uplift for at least the next year.
“This financial lifeline must also be extended to people claiming legacy benefits.
“It is unacceptable that currently many sick or disabled people and carers are wrongly excluded from the support they need to weather this economic storm.”
The StepChange Debt Charity has welcomed the Committee’s recommendations.
The charity’s head of policy Peter Tutton, who gave evidence to the Committee last week, said today: “We welcome and strongly echo the Select Committee’s findings, which clearly show just how important it is to keep the £20 uplift to Universal Credit.
“Removing the uplift would mean 74 percent of StepChange debt clients on Universal Credit would no longer have enough money to meet their essential costs, pushing their average deficit from -£60 to -£147 each month.
“This would leave more people facing agonising choices between paying their rent and feeding their families; skipping meals and turning to high cost credit just to get by.
“People’s finances have been suffering at the hands of this pandemic for nearly a year – coping strategies are exhausted, budgets stretched to their limit.
“If the uplift is withdrawn at this stage, those on Universal Credit will be faced with the lowest relative level of unemployment benefit in nearly 20 years, risking deepening inequality, threatening economic recovery and jeopardising levelling-up ambitions. It’s vital the uplift is kept.”