Democratic Rep. Joaquin Castro is considering jumping into the Texas Senate race, but he might not have the primary to himself if EMILY’s List gets its way. 

The influential group, which backs female Democrats who support abortion rights, is in talks with three potential candidates: Air Force veteran MJ Hegar, who lost a House race in 2018;  Houston City Council member Amanda Edwards; and former state Sen. Wendy Davis. 

“We would love to see a woman take Sen. [John] Cornyn on,” EMILY’s List president Stephanie Schriock told reporters Thursday. “We are in some conversations and really would like to find the candidate and then get everybody behind a strong woman to run for the U.S. Senate seat in Texas.”

Castro’s campaign did not immediately respond to a request for comment. According to Texas Monthly, Davis encouraged Castro to run and would consider running herself if he does not.  

Hegar has been mentioned as a potential Senate candidate since she raised millions last cycle in her unsuccessful race against GOP Rep. John Carter — she lost by 3 points. Hegar tweeted this week that she is “taking a very close look” at running for Senate. 

Democrats in the state view Cornyn as vulnerable, particularly after former Rep. Beto O’Rourke nearly defeated Texas’ other Republican senator, Ted Cruz, last fall, losing by less than 3 points. The Texas Democratic Party is planning to set up a “Cornyn War Room” to define the three-term incumbent early on in the campaign, the Texas Tribune reported Thursday. 

But Texas would still be a difficult state for Democrats, who haven’t won a statewide election there since 1994. President Donald Trump carried the state by 9 points in 2016.

Inside Elections with Nathan L. Gonzales rates the Texas Senate race Solid Republican. 

Watch: What race ratings really mean and how we create them