Moore said he will make an announcement from Montgomery on Thursday afternoon.
The website Politico obtained a copy of a draft email that was expected to be sent to Moore's supporters earlier this week asking them to attend the event on Thursday to hear the announcement.
"Judge has spoken with most all of you on the phone over the past few weeks and is appreciative of your warm support," Kayla Moore, Moore’s wife, wrote in the draft note.
"We will be making an official announcement regarding the (Senate) race in Montgomery this Thursday,” the draft memo read.
Moore lost a 2017 special election by a narrow margin to Doug Jones, a former federal prosecutor. Jones was the first Democrat elected to the U.S. Senate from Alabama in more than 25 years.
The election was held to fill the seat vacated by Sen. Jeff Sessions, R-Alabama, after Sessions was confirmed as U.S. attorney general.
Sessions resigned as attorney general last year. As of yet, he has not said if he is considering running for his former seat.
U.S. Rep. Bradley Byrne, former Auburn University football coach Tommy Tuberville and state legislator Arnold Mooney have all said they will run in the Republican primary for the seat.
If Moore announces he is running, he will likely not be able to count on support from President Donald Trump.
Trump, who was once a strong Moore backer, backed off on that support amid allegations of sexual misconduct by Moore.
Eight women came forward in 2017 to say Moore had acted inappropriately toward them when they were in their teens and he was in his 30s. He has denied the allegations.
Last month, Trump tweeted that Moore “probably won’t” win the race. He also said he “had nothing against” Moore.
Moore has also taken to Twitter, slamming Republican Sen. Richard Shelby, of Alabama, on Wednesday by saying that, if Shelby “would have stayed out of the 2017 race, Doug Jones would not be in the Senate now!”