The convicted family killer, in prison for the rest of his life, is researching his case and reaching out to attorneys

Chris Watts, who is in prison for killing his entire family, is weighing his legal options to decide whether to appeal his conviction.

A source close to Watts tells PEOPLE that Watts is “looking into ways to appeal” his punishment — and has been researching his case and other similar cases.

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“Obviously, it would be an uphill battle for him, because he pleaded guilty,” says the source, who has knowledge of Watts’ legal case. “And with a guilty plea, you forfeit some of your rights to appeal. But that’s not absolute, so there’s a small chance that it could work out in his favor.”

The source says that Watts has spoken with attorneys on the phone, but doesn’t have a plan for his representation. “It would cost him money that he just doesn’t have,” says the insider. “But he is still exploring his options.”

Image zoom Chris Watts CBI

Watts, 33, is serving multiple life sentences after pleading guilty last November to the August 13, 2018, murders of his pregnant wife, Shanann, 34, and the couple’s two young daughters: Bella, 4, and Celeste, 3.

In a Feb. 18 interview from inside prison, Watts gave chilling details of the murders to authorities from the Colorado Bureau of Investigation. He said his wife Shanann “may have been” praying as he strangled her to death inside their bedroom. He said he then drove his wife’s body to his job site, where he buried it in a shallow grave as his daughters waited in the car. Additionally, he claimed Bella saw him smother Celeste and screamed “Daddy, no!” at him before he killed her.

“I hear it every day, when Bella was talking to me,” Watts told detectives. “When she said, ‘Daddy, no!’”

He also said he speaks to the photos of his family in his cell and reads a book out loud to his deceased daughters every night.

Image zoom Shanann and Chris Watts Facebook

According to the insider, Watts feels that he was unable to explain some of the mitigating circumstances of what happened on the night he killed his family.

“Everything happened so fast there at the end [of the legal proceedings],” the source says. “And he’s not sure he was in the right mind to plead guilty like he did. For him, it’s not just about him getting out of jail — it’s also that he hasn’t been able to really have his day in court.”

Image zoom Celeste and Bella Watts Facebook

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Even if Watts retains an attorney licensed to practice in Colorado, he’d still have to deal with the appeal from several states away. (He’s imprisoned in Wisconsin.)