Politician Madeleine Albright and Mayim Bialik said they "stand ready" to register, in defiance of the new President.
"I was raised Catholic, became Episcopalian & found out later my family was Jewish," Ms Albright - the first woman to be named Secretary of State - tweeted on Wednesday.
"I stand ready to register as Muslim in #solidarity." The tweet gained tens of thousands of likes.
Her comments come as rumours continue to circulate about an executive order which would announce extreme vetting, a refugee ban and a ban on arrivals from seven countries, said to include Syria, Yemen and Iraq.
But there has been no mention of a register of American Muslims in recent months - something Mr Trump said he would "certainly implement" in an interview in 2015, but later distanced himself from.
It has been reported that the President will be announcing his new executive order on Thursday.
Many, including Ms Albright, a Czech immigrant, are highly critical of the move - which is rumoured to mean the US would accept no Syrian refugees.
"There is no fine print on the Statue of Liberty," she tweeted. "America must remain open to people of all faiths and backgrounds. #RefugeesWelcome."