Betfair has put the foreign secretary odds-on at 4/6 to be the next Tory party leader, even though Conservative MPs gave Mr Sunak more support in the ballot to select the final two contenders.
The former chancellor is the 6/4 underdog with Betfair.
Irish bookmaker Paddy Power priced Ms Truss at 8/15 to be the next leader, marginally ahead of Mr Sunak, on 5/4.
William Hill had Ms Truss at 4/7 and Mr Sunak at 6/4.
A Sunak supporter described the outcome of the final MPs’ ballot as “a really strong result with a clear mandate from MPs” for the former chancellor, whose tally amounted to 38 per cent of the parliamentary party, against 32 per cent for Ms Truss and 29 for Ms Mordaunt.
Mr Sunak and Ms Truss will now fight for votes among party members across the UK.
Ballot papers will be sent out from 1 August to 160,000 activists, who will choose their new leader – and the prime minister – in a secret ballot, before the result is announced on 5 September.
A poll of 493 Conservative Party members carried out earlier this month for Channel 4 News put Mr Sunak ahead by a narrow margin.
The final two contenders will face each other in a televised BBC debate on Monday at 9pm.
They will then do battle at hustings debates twice a week around the UK until September.
Ms Mordaunt congratulated her two rivals, saying: “I pay tribute to anyone who puts themselves forward for such a demanding role.
“Politics isn’t easy. It can be a divisive and difficult place.
“We must all now work together to unify our party and focus on the job that needs to be done.”