According to Wikipedia, which should be taken with a grain of salt, here are the potential nominees. Shelby and Sessions both declined:
Publicly Expressed Interest
Mo Brooks, U.S. Representative for Alabama's 5th congressional district and candidate for U.S. Senate in 2017
John Merrill, Alabama Secretary of State and candidate for U.S. Senate in 2020
Potential
Robert Aderholt, U.S. Representative for Alabama's 4th congressional district
Will Ainsworth, Lieutenant Governor of Alabama
Lynda Blanchard, former United States Ambassador to Slovenia
Katie Britt, former Chief of Staff to U.S. Senator Richard Shelby
Bradley Byrne, former U.S. representative for Alabama's 1st congressional district and candidate for U.S. Senate in 2020
Tommy Hanes, state representative
Steve Marshall, Alabama Attorney General
Gary Palmer, U.S. Representative for Alabama's 6th congressional district
Jessica Taylor, businesswoman, attorney, and candidate for Alabama's 2nd congressional district in 2020
If their politics are going to suck anyway, might as well be Jessica Taylor
