An early grassroots favourite to succeed Johnson, the 49-year-old came close to beating Truss to make the final run-off against Sunak in the summer.
The former defence and trade junior minister was a strong Brexit supporter and a key figure in the 2016 "Leave" campaign.
But she faced criticism during the recent leadership race, with some MPs dismissing her as ineffective in government roles.
Mordaunt's profile rose earlier this week after she was dispatched in place of Truss to answer an urgent question in parliament from the Labour opposition about the recent economic turmoil.
Mordaunt was seen as coping well with the febrile House of Commons session, where she was forced to confirm the absent prime minister was "not (hiding) under a desk".