It is understood she has held talks with Jeremy Hunt and assured him he can stay on as Chancellor if she becomes prime minister.
She also assured Mr Hunt she would deliver the medium-term fiscal plan as proposed on October 31, according to a source close to the Commons Leader.
Liz Truss resignation: 'Wave of revulsion' in Scotland if Boris Johnson returns to Downing Street, says SNP's Ian Blackford
Announcing her bid for the Tory leadership, Penny Mordaunt tweeted: “I’ve been encouraged by support from colleagues who want a fresh start, a united party and leadership in the national interest.
“I’m running to be the leader of the Conservative Party and your Prime Minister – to unite our country, deliver our pledges and win the next GE.”
Mordaunt came third in the last leadership contest that saw Liz Truss announced as Prime Minister, but Mordaunt secured strong support from her fellow MPs and just missed out on making it to the final two.
After backing Truss Liz she was appointed leader of the House of Commons and Lord President of the Privy Council and presided over the Accession Council for the new king.
Former cabinet minister Andrea Leadsom has backed Penny Mordaunt to be the new Tory leader, citing her “compassion” and “determination”.
Quoting a post from Ms Mordaunt announcing her bid, Ms Leadsom tweeted: “Delighted by this!
“Penny has the experience, the compassion and the determination to lead our country to a bright future!”
She added the hashtag #PM4PM.