Ministers will be told by Theresa May they should be keeping cabinet discussions private, Number 10 says.
Following several leaks and briefings over the weekend, ministers will be “reminded” of their responsibilities when cabinet meets on Tuesday.
On Sunday Chancellor Philip Hammond suggested colleagues opposed to his approach to Brexit had been briefing against him.
It followed press reports of his cabinet remarks on public sector pay.
BBC political editor Laura Kuenssberg said several factors were at play, including some ministers’ belief Mr Hammond was trying to slow down the Brexit process, and Mrs May’s weakened position after the general election.
“With the PM’s authority so reduced it’s like the teacher has left the classroom and the teenagers have started a big rumble – and they are partly scrapping with each other because several of them fancy taking the controls themselves,” she added.
Mrs May’s spokesman declined to discuss the content of the leaks, but told reporters: “Of course, cabinet must be able to hold discussions of government policy in private and the prime minister will be reminding her colleagues of that at the cabinet meeting tomorrow.”
Speaking on BBC Radio 4’s Today programme, Transport Secretary Chris Grayling attempted to play down suggestions of cabinet splits over Brexit and criticised those who have been briefing about its meetings.
“I don’t see these great divisions that are suggested to me in the Sunday newspapers and I have to say I think all of this is somewhat overplayed,” he added.
One backbencher, Nadine Dorries, tweeted that she would rather see ministers sacked than another leadership contest.
Responding to the leaks on Sunday, Mr Hammond refused to comment on newspaper reports that he said public sector workers were “overpaid” and told his colleagues to “focus on the job at hand”.
Another minister, International Trade Secretary Liam Fox, attacked the “self-indulgence” of those doing the leaking, adding that it had left Tory backbenchers “furious”.