The report, commissioned by David Cameron in January 2016, is understood to have been in Mrs May’s possession for at least six months.
She responded to a parliamentary question by saying “ministers are considering advice on what is able to be published and will report to parliament with an update in due course”.
Home Office sources said the report does include references to Saudi Arabia but insisted the Gulf state was not the major focus.
The report was part of a deal Mr Cameron struck as prime minister with the Liberal Democrats to secure their support for extending British airstrikes against ISIS targets in Syria in December 2015.
The Home Office extremism analysis unit – presided over by Mrs May at the time – was asked to examine the origins and scale of funding for UK extremist groups, with an additional remit to follow international funding streams.
The Lib Dems have kept up pressure on the Conservatives to publish the report, while government insiders have countered that some of the material concerning terror and extremism financing is too sensitive to be made public.
Tim Farron, the outgoing Liberal Democrat leader, said: “The government are covering up this report. It’s a scandal that this is sitting in Downing Street gathering dust. What has the Prime Minister got to hide?
“I believe this report will be deeply critical of Saudi Arabia and that is why it is being hidden from the public. The government seems too desperate to keep Saudi Arabia happy rather than stand up to them.”
In May this year Tom Brake, the Lib Dem foreign affairs spokesman, wrote to Mrs May asking her to confirm that she would not shelve the investigation.
He wrote: “It is no secret that Saudi Arabia in particular provides funding to hundreds of mosques in the UK, espousing a very hardline Wahhabist interpretation of Islam.
“It is often in these institutions that British extremism takes root. Now is not the time to brush this under the carpet once more.”
A Home Office source said it was wrong to suggest the report was being suppressed because of a focus on Saudi Arabia.