As if the ultimate direction of Brexit was not enough for Brits to contend with, now speculation is mounting that British Prime Minister Theresa May could resign — throwing the whole process into further doubt.

May met her closest ministers Monday morning and is expected to update the House of Commons on her Brexit strategy in the afternoon, amid continuing turbulence and confusion over the U.K.'s departure from the EU.

There have been reports in various U.K. media outlets that May is facing another mutiny within her own party.

On Sunday, May met with influential Brexiteers in her Conservative Party and, according to some reports, gave her word that she would give a date for her resignation in return for their support in a third possible vote on her Brexit deal, formally known as the "Withdrawal Agreement." Whether a third vote will even take place this week remains up in the air as it's doubtful that there's enough support to pass the deal.

Downing Street refused to comment on speculation over May's political future although pressure is rising on her both inside euroskeptic circles and outside. The widely-read tabloid newspaper The Sun, which has previously supported May, used its front page on Monday to urge the prime minister to quit, with the headline "Time's Up, Theresa."

The paper said while she had "shown courage" in office, she was facing "fresh pressure" and that "the PM is being urged to vow she'll resign in a last-ditch bid to convince Brexiteers they should back her deal in the Commons this week."

Sun Tweet:

Several senior ministers said Monday they do not want May to resign, casting doubts over the rumored coup. Nonetheless, her position remains "fragile," according to Constantine Fraser, a European political research analyst at TS Lombard.

"Despite her Cabinet seemingly abandoning an attempt at a coup over the weekend, May's position is still extremely fragile," he said in comments emailed to CNBC.

"For now, what she has in her favor is that time is short, there is little agreement in the (Conservative) party as to who should replace her, and it not obvious what difference a change of prime minister would make to the country's immediate predicament. For her rivals, she also makes a convenient scapegoat for the failings of the Withdrawal Agreement."