Mrs May told MPs last week that she wanted the inquiry - which is without a chairman following the resignation of two previous appointees - to be given extra powers.
That could mean waiting for a chairman to be appointed for the inquiry panel, who would then request statutory powers, or setting up a new inquiry panel under statutory terms.
The third option of a Royal Commission - as some want - would not have the powers of a statutory inquiry under the 2005 Inquiries Act and would be ''legally more risky''.
Previous appointments as inquiry chairwomen Fiona Woolf and Baroness Butler-Sloss resigned following claims about their perceived closeness to establishment figures.
In her letter to the panel members, reported by the investigative website Exaro News, Mrs May said: "I am currently considering these options and I appreciate this has implications for members of the panel."
In a reply to Mrs May obtained by Exaro, panel member Sharon Evans of the child safety group Dot Com Children's Foundation said: "I, like other members of the panel, feel devastated at the prospect of the independent inquiry being halted as it has been made clear to us 'off the record' that the panel will be stood down in the New Year."
A Home Office spokesman said: "The Home Secretary is determined that appalling cases of child sexual abuse should be exposed so that perpetrators face justice and the vulnerable are protected.
"She is absolutely committed to ensuring the Independent Panel Inquiry into Child Sexual Abuse has the confidence of survivors.
"The Home Secretary is also clear that we have to balance the need to make progress with the need to get this right."