A recent YouGov poll showed that around two-thirds of respondents had an unfavourable opinion of him.
Johnson has kept a low profile since resigning, taking several holidays and giving a paid speech in the United States last week followed by his now-shortened trip to the Caribbean.
He was thought to favour Truss in the first Tory leadership contest -- although his former top aide Dominic Cummings, now an arch-critic, argued that this was because he expected her tenure to be disastrous and short-lived, paving the way for his return.
- PENNY MORDAUNT -
The current cabinet member was the first to formally declare she was standing, in a tweet on Friday.
She followed up Saturday with a slickly produced campaign video charting her life story, growing up in, and then representing in parliament, the south coast city of Portsmouth.
She also appeared on the BBC's flagship Sunday political talk show, claiming she was best placed to reunite her fractured party.
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".
