Ministers had hoped the existing early release scheme would buy them 12 months.
But the riots this year mean prisons are expected to be full again next summer, before any changes to sentencing can be made.
In the long term, ministers want to consider sentencing changes that could reduce crime.
Ending or moving away from short sentences could have a particular effect on the number of women in jail, after the Prison Reform Trust found last year that over half (58%) of jail terms given to women in 2022 were for less than six months.
Ministry of Justice figures show, external more than half of adults (57%) released from prison sentences of less than 12 months went on to reoffend.
One Ministry of Justice source said the government would be encouraging the reviewer “to follow the evidence in terms of how sentencing can cut crime”.
“Prisons are creating better criminals, not better citizens,” the source said.
A solicitor who was seen as being on the centrist wing of the Conservative Party, Gauke could be viewed as a contentious choice to lead the review.
In 2019, he made a series of speeches to call for a shift away from short prison sentences and towards punishment in the community.
But Gauke’s successor, Robert Buckland, said he did not believe abolishing short sentences was the right way forward.
