Philip Hammond has admitted Theresa May’s Brexit deal may not be able to get through the Commons, as senior ministers moved to quell speculation the prime minister could be forced out within days in a cabinet revolt.

With the prime minister preparing to meet a group of senior Tory rebels at her Chequers country retreat, the chancellor told Sky News’s Sophy Ridge on Sunday that Conservative colleagues were “very frustrated” and “desperate to find a way forward”.

But as two ministers who had been named as possible interim successors, Michael Gove and David Lidington, played down speculation about the prime minister’s future, Hammond said that talk of pushing May out was “frankly self-indulgent at this time”.

The chancellor – who had been named as one of a group plotting to force her out in a crunch cabinet meeting on Monday – refused to be drawn on whether his colleagues had approached him asking him to intervene.

The chancellor – who also said a second referendum “deserves to be considered” – instead made clear that May’s Brexit deal was in serious trouble. He said: “I’m realistic that we may not be able to get a majority for the prime minister’s deal and if that is the case then parliament will have to decide not just what it’s against, but what it is for.”

Hammond’s qualified support came as it emerged that May was planning to meet Brexit rebels Boris Johnson, Dominic Raab, Jacob Rees-Mogg, Steve Baker and Iain Duncan Smith at Chequers as she tries to find a way to cling on to her job and get her deal through the Commons.

David Davis, who had swung round to supporting her deal, and the loyalist former cabinet minister Damian Green are also due to attend the meeting with May and her de facto deputy, David Lidington, and the ministers Michael Gove and Steve Barclay.

Earlier on Sunday Lidington was forced to deny he wanted to take over as interim prime minister following intense speculation that a cabinet group including Hammond wanted him to replace May.

In an interview given from his Buckinghamshire constituency, he denied any involvement in a plot against the prime minister, saying there had been “a lot of far-fetched speculation around this morning” and insisting he supported getting her Brexit deal through parliament.

“I don’t think that I’ve any wish to take over from the PM who I think is doing a fantastic job,” he said. “I tell you this: one thing that working closely with the prime minister does is cure you completely of any lingering shred of ambition to want to do that task.”

Later, Gove, the environment secretary, said he “absolutely” supports the prime minister and added: “It’s not the time to change the captain of the ship.”

“I think this is a time for cool heads. But we absolutely do need to focus on the task at hand, and that’s making sure that we get the maximum possible support for the Prime Minister and her deal,” he told the BBC.

Hammond said the report in the Sunday Times about a cabinet plot was not accurate. “That’s not right at all. My position is that this isn’t about individuals, this is about how we move forward.”

As well as Hammond, Greg Clark, the business secretary, Amber Rudd, the work and pensions secretary, and David Gauke, the justice secretary, were named as plotters. But other reports suggested Gove was also willing to take over as a caretaker leader and had the backing of some Brexit supporters.

Cabinet anxieties about May and her ability to maintain control of the stalled Brexit process remain acute, with few in Westminster believing she can get a revised version of her deal through the Commons in the coming days.

Duncan Smith said the idea of a coup “would be unacceptable to my colleagues” and accused cabinet members of breaching collective responsibility by briefing against May.

“If there is to be a leadership change,” Duncan Smith said in an interview on BBC One’s The Andrew Marr Show, “it has to be done through the correct process, with the membership deciding, not some ghastly five- to six-person cabal.”

Duncan Smith also held out a glimmer of hope for May’s deal, saying: “I will recommend that colleagues should keep their counsel on this one.” He said a final decision would have to be balanced against whether a no-deal Brexit remained on the table.

Barclay, the Brexit secretary, said Duncan Smith and Ken Clarke, who “reflect a wide spectrum of views on Europe”, had both said that a change of leadership would be a massive distraction.

He said there had been “a lot of emotion” in the weekend newspapers and it would be for May to judge whether ministers had breached cabinet collective responsibility by briefing that she should quit.

The chancellor said parliament would be given the chance to hold indicative votes on alternatives to May’s deal this week, including cancelling Brexit by revoking article 50, a no-deal exit on World Trade Organization terms, remaining in the customs union, and remaining in the customs union and close to the single market.

“One way or another, parliament is going to have the opportunity this week to decide what it is in favour of, and I hope that it will take that opportunity – if it can’t get behind the prime minister’s deal – to say clearly and unambiguously what it can get behind,” he said. Hammond said a decision had not yet been made on whether Tories would be given a free vote on the matter. He said he believed only two options should be taken off the table: no deal and no Brexit.

The chancellor refused to rule out a second referendum. “I’m not sure that there’s a majority in parliament for a second referendum but it’s a perfectly coherent proposition,” he said. “Many people will be strongly opposed to it, but it’s a coherent proposition and it deserves to be considered along with the other proposals.”

The Labour MP Jon Trickett, the shadow Cabinet Office minister, said: “Philip Hammond’s interview was extraordinary. The chancellor signalled that the deal they’ve worked on for nearly three years is dead and junked the idea of no deal – which Theresa May has held on to from the beginning.”