- Tory party donor Jon Moynihan, aide Ruth Porter, ex-Vote Leave's Matthew Elliott and think tank boss Mark Littlewood are said to be on the list.
- A spokesman for Ms Truss said it would not be "appropriate" to comment.
Former Prime Minister Liz Truss has been criticised by two former aides for choosing to submit a list of resignation honours.
Ms Truss, who spent only 49 days in office, has put forward four people, the Sun and i reported.
Tory party donor Jon Moynihan, aide Ruth Porter, ex-Vote Leave's Matthew Elliott and think tank boss Mark Littlewood are said to be on the list.
A spokesman for Ms Truss said it would not be "appropriate" to comment.
Both Labour and the Liberal Democrats have called on Prime Minister Rishi Sunak to block the move.
Any outgoing prime minister is able to recommend people for honours after they've resigned, although not all have chosen to.
Allies say Ms Truss's list is "modest" but former aides are among those expressing anger that she is making any nominations at all.
Two former advisers told the BBC they did not think she should be putting anybody forward, given her short time in office.
One said they were "relieved to no longer be working for her and having to defend the indefensible".
Labour's deputy leader Angela Rayner called it a "list of shame", saying the former PM and her supporters "took a wrecking ball to the economy in a disastrous six-week premiership that has left millions facing mortgage misery".
Wendy Chamberlain MP, the Lib Dems' chief whip, described the move as "truly remarkable", adding: "Rishi Sunak must block these honours immediately as allowing Truss to dish out positions of influence shows a stunning lack of humility."
The BBC has not confirmed the names of those reported to be on the list.
Mr Littlewood is director of the Institute of Economic Affairs, a free-market supporting think tank that was associated with Ms Truss and her former chancellor Kwasi Kwarteng.
Mr Elliott, who helped found the Taxpayers Alliance group, which campaigns for lower taxes, was chief executive of the main pro-Brexit campaign during the 2016 referendum.
Ms Porter ran Ms Truss' Tory election leadership campaign and briefly served as her deputy chief of staff in No 10.
The register of MPs' financial interests shows that Mr Moynihan donated £50,000 in two separate transactions to her Tory leadership campaign.
It's unclear when Ms Truss' nominations would be assessed by the Cabinet Office, which is already considering nominations from Boris Johnson.
King Charles is also expected to hand out honours to mark his coronation.
Outgoing prime ministers can ask the monarch to bestow peerages, knighthoods, and other honours on any number of people of their choosing.
Mr Cameron nominated 59 people for honours when he resigned, while Ms May nominated 51.