He says, "We'll see how she does, I wish her well. I hope she does well. I'd love to run against her."
Trump has been lambasting Warren since his 2016 campaign, when he began derisively labeling her "Pocahontas" in a shot against her claims of Native American heritage.
Trump says Warren "did very badly in proving that she was of Indian heritage," adding that her decision earlier this year to release a DNA analysis "didn't work out too well."
Sen. Elizabeth Warren is taking the first major step toward launching a widely anticipated campaign for the presidency. She is hoping her reputation as a populist fighter can help her navigate a Democratic field that could include nearly two dozen candidates.
The Massachusetts Democrat says she's forming an exploratory committee for the 2020 campaign. She's the most prominent Democrat yet to make such a move.
Warren burst onto the national scene a decade ago during the financial crisis with calls for greater consumer protections, and quickly became one of the party's more prominent liberals.
Now, as a likely presidential contender, she is appealing to the party's base. A video released Monday announcing her move notes the economic challenges facing people of color along with images of a women's march and Warren's participation at an LGBT event.