The chief whip and the deputy chief whip reportedly resigned, and then unresigned, ITV News understands.
The Conservative chief whip and the deputy chief whip remain in post, Downing Street said on Wednesday night.
Wendy Morton, MP for Aldridge-Brownhills in the West Midlands since 2015, was appointed chief whip by Ms Truss just six weeks ago.
As chief whip, she is responsible for maintaining discipline within the Conservative party.
Her deputy, Craig Whittaker, was also believed to have stepped down from his post.
But ITV News Political Editor Robert Peston has since said that the pair "do still have their jobs," and have effectively unresigned.
Earlier, Peston said that there was "total confusion" at No 10. After hearing the news of the resignations from a senior government member, a Downing Street source told him they have "no idea".
During the debate on Wednesday afternoon Labour's Thangam Debbonaire asked if “strong rumours” the government’s chief whip has resigned following a vote on Labour’s fracking motion could be confirmed.
The shadow Commons leader said: “There are very strong rumours that the government chief whip has apparently resigned. I wonder if it is possible to get some clarity more than rumours.”
She added: “I seek your guidance… given that this is a matter of parliamentary discipline.”
Deputy Speaker Dame Eleanor Laing replied: “She raises a point as to whether a member of the government has resigned. I have not been given any such information. I know no more than that and it is not a point of order for the chair."
The reported withdrawn resignations followed the resignation of Home Secretary Suella Braverman, who stepped down on Wednesday afternoon after sending "an official document from my personal email to a trusted parliamentary colleague." She said this breach of security protocol meant she had to resign from her role.
In her resignation letter Ms Braverman took a swipe at the government, saying she was concerned about its direction.
Ms Braverman was later replaced by Grant Shapps.