The UK has committed to reducing emissions by 68 per cent by 2030 — a target that is seen as one of the most ambitious among developed nations.
But the prime minister will in the coming days pledge a steeper cut of 78 per cent by 2035 compared with 1990 levels, according to the Financial Times.
The paper, quoting people who had been briefed on the plan, said the announcement would be made this week ahead of a major US summit on Thursday where President Joe Biden is expected to set out a new US target for reducing emissions.
But Mr Johnson has been urged to make international climate agreements legally binding after warnings from scientists that the UK doesn’t have a plan to meet its commitments.
Climate experts and scientists have drawn up draft legislation that could enshrine the Paris Agreement in domestic law and commit the government to produce a plan to meet it.
Despite support from over 118 MPs and peers, the government is denying the Commons parliamentary time to discuss the legislation.
More than 100 climate experts wrote to the prime minister on Monday demanding action.
Mr Johnson’s new target, if confirmed, would be in line with the recommendations of the Climate Change Committee, published last year, for the government's sixth carbon budget.
In its report, the committee said that it would effectively bring forward by 15 years the UK's commitment to getting to an 80 per cent reduction.
In order to be achieved, it said that there would have to be more electric vehicles, an extension of offshore wind power generation, a reduction in meat and dairy consumption and the planting of new woodland.
The reported move comes at a time when the government is anxious to give a clear lead on climate change in the run-up to the Cop26 talks in Glasgow in November.
The Department for Business, Energy and Industrial Strategy said that ministers would be making an announcement "shortly".
A spokesperson said: "We will set our ambition for carbon budget six shortly, taking into account the latest advice from the Climate Change Committee."
For Labour, shadow business secretary Ed Miliband said the government had repeatedly failed to match ambitious promises on emissions with effective action on the ground.
"While any strengthening of our targets is the right thing to do, the government can't be trusted to match rhetoric with reality," he said.
"We need a government that treats the climate emergency as the emergency it is.
"This year, as hosts of Cop26, the UK has a particular responsibility to lead the world and show the way forward for a greener future. This government isn't up to the task."