"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.
A number of people vowed to stand in solidarity with America`s Muslim population after Mr Trump`s election in November, but Ms Albright`s tweet appears to have inspired others to speak out - including Ms Bialik, who stars as Amy Farrah Fowler in the hit series The Big Bang Theory, one of America`s most popular sitcoms.
"I`m Jewish. I stand ready to register as a Muslim in #solidarity if it comes to that," she wrote.
Later, the outspoken Trump critic added: "If we`re registering people who you think are a threat, register white males too, since most serial killers & mass shooters are white males."
Actress Mayim Bialik, who plays Amy Farrah Fowler in The Big Bang Theory, is an outspoken Trump critic
It has been reported that the President will be announcing his new executive order on Thursday.
"Look, the president has talked extensively about extreme vetting," White House spokesman Sean Spicer said, promising "more action this week".
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 & backgrounds. #RefugeesWelcome."
Mr Trump previously spoke of banning any Muslim from entering the United States.
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