Penny Mordaunt, who is currently Minister for Disabled People, is the favourite to replace Ms Patel as Theresa May attempts to retain the balance between Leavers and Remainers in her Cabinet.
As only female MP who is a Royal Navy reservist, she was also touted as a possible replacement for Sir Michael Fallon after he resigned as defence secretary last week.
Ms Patel already apologised to Mrs May on Monday for failing to disclose a series of 12 meetings with senior Israeli figures during a family holiday in the country in August.
In her resignation letter, she said: “While my actions were meant with the best of intentions, my actions also fell below the standards of transparency and openness that I have promoted and advocated.”
Conservative MP Jacob Rees-Mogg suggested disgruntled Remainers could be behind the leak that led to the downfall of Ms Patel.
European Union leaders are preparing for the possible “fall of Theresa May before the new year” and either “a change of leadership or elections leading to a Labour victory”.