The Prime Minister is facing a second reshuffle in a week as she attempts to reassert her authority following Priti Patel's resignation.
Theresa May accepted the resignation of her international development secretary after Ms Patel acknowledged that secret meetings with senior Israeli figures "fell below the high standards" expected of a Cabinet minister.
The Prime Minister faces a politically sensitive challenge in replacing prominent Brexit-backer Ms Patel.
Her decision to appoint Gavin Williamson as Defence Secretary after Sir Michael Fallon's resignation last week was openly criticised by some of her MPs and Mrs May will be anxious to avoid creating further unrest in her fragile administration.
The Prime Minister could be keen to replace Ms Patel with another Brexit-backer in order to placate Eurosceptic MPs on the Conservative benches and maintain the current balance within the Cabinet.
Prominent Tory Brexiteer Jacob Rees-Mogg suggested that disgruntled Remainers could have been behind the leak which led to Ms Patel's downfall.
He said that generally "conspiracy theories are wrong" because "people aren't behaving according to some grand Marxist plan".
"But nonetheless there are still some people who are still very bitter about the result a year ago and inevitably that colours their behaviour," he told BBC's Newsnight.
"If you go into how did Priti Patel's visit come out in the first place, was it leaked by the Foreign Office, was it leaked by somebody at the Foreign Office who resented her and probably the Foreign Secretary's role in Brexit, you may find something."
Ms Patel's replacement would not necessarily have to be an ardent Brexiteer, he said. "As long as it's somebody who has accepted that Brexit is happening and will support it properly and won't be a frightful Eeyore I don't think there will be a problem."
With Brexit talks resuming in Brussels, Mrs May's domestic difficulties are having repercussions in European capitals, with preparations reportedly being made in case her administration collapses.
The Times quoted an unnamed European leader as saying: "Britain is very weak and the weakness of Theresa May makes negotiations very difficult."
Witham MP Ms Patel was forced to cut short an official trip to Africa and return home for a showdown with Mrs May on Wednesday at which it was made clear her Cabinet career was over.
Her downfall came after it emerged she had a series of 12 engagements with senior Israeli figures - including Prime Minister Benjamin Netanyahu - during a holiday in the country in August.
She then held two additional meetings, one in the UK and one in the US, following her return from Israel.
In a further development, the Israeli Haaretz newspaper reported that during her stay in the country she visited an Israeli military field hospital in the occupied Golan Heights.
Britain, like other members of the international community, has never recognised Israeli control of the area seized from Syria in the 1967 Six-Day War.
The meetings, without officials and in relation to one of the most sensitive areas of foreign policy, led to Ms Patel apologising and being given a dressing down by Mrs May on Monday.
But subsequent disclosures added to pressure on Ms Patel, culminating in the meeting in Downing Street which lasted around 30 minutes.
In her resignation letter Ms Patel said: "I accept that in meeting with organisations and politicians during a private holiday in Israel my actions fell below the high standards that are expected of a Secretary of State."