As well as this prisons strategy, the government hopes a separate review into sentencing could be a longer-term solution to reduce demand on prisons.
The review of prison sentences is being led by David Gauke, a former Conservative justice secretary.
The review is expected to consider scrapping short sentences and toughening up community orders as an alternative to jail. It will report back next spring.
Asked by the Today programme whether some people currently in prison might not be in the future, Mahmood said it was a possibility.
"Yes... We will have to expand the range of punishment available outside of prison, that does mean that we will have more offenders monitored outside," she said.
"But I want to make sure that when we are not putting someone in prison but they're being punished outside, that that is still a punishment they can have confidence in."
The Conservative government had pledged to build 20,000 new prison places by 2026.
HMP Prison and Probation Service had created more than 6,518 as of September.
The Labour government has pledged to create the remainder - about 14,000 - by 2031, a promise already made during the election campaign
Last week, the National Audit Office released a critical report saying that Boris Johnson's government pledge to create an extra 20,000 cell spaces was now not expected to be met until 2031 – about five years later than promised. It also said the scheme was running £4.2bn over budget.