Downing Street also did not deny reports that Mr Johnson is backing a new tax to pay for social care reforms or that a cap on payments could form part of his plans.
Mr Johnson is under increasing pressure to offer details on the plan, which he said was ready on the steps of Downing Street in 2019.
Lord Bethell’s remarks came as peers considered calls for a state-owned company to provide insurance for homeowners against having to sell their properties to pay for elderly social care.
Speaking in the debate, Lord Bethell said: “Can I say to Baroness Watkins of Tavistock that the Prime Minister has been very clear that we need a long-term plan for social care and, as she will know from today’s papers, the details are emerging as we speak.”
A No 10 spokesman said: “I’m not going to start commenting on speculation. No decisions have been made and we will set out the details later this year.”
Conservative former social security secretary Lord Lilley voiced concerns over the reported proposals and its impact on red wall voters.
Moving his Elderly Social Care (Insurance) Bill, Lord Lilley said: “At the last election, Labour promised to set a cap of £100,000 on the maximum cost anyone would incur while in residential care for social care.
“And today we read in the Daily Telegraph that the Government could as early next week adopt that policy, hoping no doubt for bipartisan support.
“But it’s not Labour’s support they need but that of homeowners and the general public.
“The problem is that a £100,000 cap would be fine for the owner and heirs of a £10 million mansion in Mayfair even if they spent decades needing substantial care for dementia.