"I can't find out anything more shocking than I've already learned," Sharpton told the Daily News, which on Sunday reported the link based on genealogists' findings.
Sharpton's spokesman, Rachel Noerdlinger, confirmed Monday for The Associated Press that Sharpton plans to pursue DNA testing, but had no further details.
CBS News Radio correspondent Peter King reports that Sharpton said he will interview the researchers and the reporter on-air and take calls about the topic.
Sharpton and Thurmond didn't appear to have much in common: Thurmond ran for president in 1948 as a segregationist. Sharpton ran for president in 2004 calling for racial equality. Sharpton learned about the connection last week.
"It was probably the most shocking thing in my life," Sharpton said at a news conference Sunday, the day the Daily News reported the link.
Professional genealogists who work for Ancestry.com found that Sharpton's great-grandfather, Coleman Sharpton, was a slave owned by Julia Thurmond, whose grandfather was Strom Thurmond's great-great-grandfather. Coleman Sharpton was later freed.
"Based on the paper trail, it seems pretty evident that the connection is there," said Mike Ward, a genealogist with Ancestry.com who called the link "amazing."
Ancestry.com's chief family genealogist, Megan Smolenyak, said Sharpton would need to match his DNA with a present-day descendant to see if they are biologically related.
"I think the odds are slim he would match," Smolenyak told the News. "There is no particular evidence to suggest that there is a direct relationship between the two (black and white) Sharpton families to suggest they share a common ancestry. But, given the legacy of plantation society, you can't rule it out."
The revelations surfaced after Ancestry.com contacted a Daily News reporter who agreed to have his own family tree done. The intrigued reporter then asked Sharpton if he wanted to participate. Sharpton said he told the paper, "Go for it."
The genealogists, who were not paid by the newspaper, uncovered the ancestral ties using a variety of documents that included census, marriage and death records.
Strom Thurmond, of South Carolina, was once considered an icon of racial segregation. During his 1948 bid for president, he promised to preserve segregation — and in 1957 he filibustered for more than 24 hours against a civil rights bill.
But Thurmond was seen as softening his stance later in his long life. He died in 2003, at 100. One of the longest-serving senators in history, he was originally a Democrat but became a Republican in 1964.
His children have confirmed that he fathered a biracial daughter. Essie Mae Washington-Williams' mother was a housekeeper in the home of Thurmond's parents.
Sharpton said he met Thurmond only once, in 1991, when he visited Washington, D.C., with the late James Brown, who knew Thurmond. Sharpton said the meeting was "awkward."
"I was not happy to meet him because what he had done all his life," Sharpton said.
Sharpton said he hadn't attempted to contact the Thurmond family. As far as he knew, he said, the family hadn't tried to call him, either.
Some of Thurmond's relatives said the nexus also came as a surprise to them. A niece, Ellen Senter, said she would speak with Sharpton if he were interested.
"I doubt you can find many native South Carolinians today whose family, if you traced them back far enough, didn't own slaves," Senter, of Columbia, S.C., told the Daily News.
She added: "And it is wonderful that (Sharpton) was able to become what he is in spite of what his forefather was."
Telephone messages left by The Associated Press for Strom Thurmond Jr. and for an attorney who once represented Thurmond's biracial daughter were not immediately returned Sunday.