More than 100 members of parliament (MPs) belonging to the governing Conservative Party are ready to submit letters of no confidence in Truss to Graham Brady, the head of the Conservative Party's committee which organizes the leadership contest, the tabloid reported, quoting unnamed sources.
Britain, engulfed in a political crisis, has lost three prime ministers since it voted to leave the European Union in 2016.
The MPs will urge Brady to tell Truss that "her time is up" or to change the political party rules to allow an immediate vote of confidence in her leadership, Daily Mail reported.
Brady is said to be resisting the move, arguing that the Truss, along with newly appointed Chancellor Jeremy Hunt, deserve a chance to set out economic strategy in a budget on Oct. 31, the report added.
Separately, The Times reported that some lawmakers have held secret discussions on replacing Truss with a new leader.
Truss, who won the Conservative Party leadership last month after promising to slash taxes, is fighting for her political survival after ditching key parts of the program.
The chaos has fueled discontent in the party, which is falling behind the opposition Labor Party in opinion polls.
MA/PR