The lawsuit could be filed as early as Thursday, though it's unclear as of Wednesday night whether that will occur.
A spokesman for the DOJ declined to issue a comment.
Texas Senate Bill 8 went into effect on Sept. 1. The bill, which prohibits abortions once a heartbeat can be detected in a fetus, also does not make exceptions for rape or incest.
On Tuesday, as Gov. Greg Abbott signed the controversial voting bill, he was asked about the lack of a rape exception in the abortion law.
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"Let's make something very clear, rape is a crime, and Texas will work tirelessly to make sure that we eliminate all rapists from the streets of Texas by aggressively going out and arresting them and prosecuting them and getting them off the streets," Abbott stated. "So, goal number one in the state of Texas is to eliminate rape, so that no woman no person will be a victim of rape."
Texas' abortion law also allows private citizens to personally sue anybody they think is either trying to get an abortion illegally or anybody helping them.
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Abortion rights advocates say the Texas law will force many women to travel out of state for abortions, if they can afford to do so and also navigate issues including childcare and taking time off work. It is also expected to increase the number of women seeking to self-induce abortions using pills obtained by mail.