High-level Democrats said Rep. Alexandria Ocasio-Cortez (D-NY) may primary Senate Minority Leader Chuck Schumer (D-NY) or Sen. Kirsten Gillibrand (D-NY), according to a report.

Top Democrats reportedly told Axios that they expect the progressive and freshman Rep. Ocasio-Cortez to primary Sen. Schumer in 2022 or Sen. Gillibrand in 2024. Gillibrand continues to campaign for the 2020 Democrat presidential nomination, despite her low polling numbers across the country.

Ocasio-Cortez has made national fame for her primary victory against former Rep. Joe Crowley (D-NY), who was expected to one day hold a high-ranking House leadership position such as House speaker or House majority leader.

The report arises as a Harris poll for Axios found a rising interest in socialism, especially among women. The survey found that 55 percent of women aged 18 to 54 approve of more progressive policies.

Corbin Trent, Ocasio-Cortez’s communications director, said the New York lawmaker wants to move the party towards more progressive issues, such as Medicare for All and the Green New Deal.

However, Trent cautioned that they do not eye a potential primary fight in the near future.

“Having worked on her campaign, I don’t think we’re going to be moving to a different role any time soon,” Trent said.

While Ocasio-Cortez might remain popular in her home district, she might have more trouble running for statewide office.

A Siena poll found that 47 percent of Democrats viewed the New York lawmaker favorably, compared to 30 percent of Democrats who did not view her in a positive light. While Ocasio-Cortez has a 43 percent favorability rating in New York City, she has a 25 percent favorability in the New York City suburbs and 21 percent favorability in Upstate New York.

Further, while she has a 47 percent favorability rating among black voters and 47 percent favorability among Latino voters, she has a 29 percent favorability among white voters, 27 percent favorability among Catholics, and 16 percent among Jewish voters, which might serve as a problem when running for a statewide office such as the U.S. Senate.

However, Ocasio-Cortez might sooner face a primary of her own than face off against Schumer or Gillibrand.

Former Rep. Crowley said in May that Ocasio-Cortez will likely face a primary challenger in 2020.

“I suspect she probably will,” Crowley said and added that “there hasn’t been much communication between” them.