CBS News has learned former Attorney General Jeff Sessions is "seriously considering" a campaign to win back his former U.S. Senate seat, according to multiple people familiar with his thinking.

A spokeswoman for Sessions declined to comment early Tuesday. His Washington-based attorney did not immediately return requests for comment.

"He is seriously considering a campaign," said a Republican operative familiar with Sessions's thinking, who stressed that whoever Republicans nominate is set to defeat Senator Doug Jones, Democrat of Alabama, widely considered to be the most vulnerable Democratic incumbent facing re-election next year given the GOP dominance of Alabama and strong support in the state for President Trump.

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Sessions vacated the seat to become President Trump's first attorney general. Mr. Trump, unhappy with Sessions' recusal from the investigation into Russian interference in the 2016 presidential election, ultimately forced him to resign the day after the 2018 midterm elections.

Other people confirmed Sessions is thinking about a campaign.

News of Sessions' interest in the race was first reported by Politico.

Jones is seeking a full term, after winning his seat in late 2017 in a race that drew global attention because of allegations of sexual misconduct and assault against Republican candidate Roy Moore. He admitted to relationships with younger women when he was in his 30s, but denied ever assaulting anyone.

Sessions has until November 8 to file paperwork to run. If he joins the fray, he would face five other Republican contenders: Moore, who is trying yet again, plus Representative Bradley Byrne, former Auburn University football coach Tommy Tuberville, Alabama Secretary of State John Merrill and State Representative Arnold Mooney.

Eleanor Watson contributed to this report.