Others on Haley's list include Reps. Tim ScottTimothy (Tim) Eugene ScottSenators demand cyber deterrence strategy from Trump CNN's Bakari Sellers: Democratic leadership is 'old and stale' Politicians, faith leaders react to passing of Billy Graham MORE (R-S.C.) and Trey GowdyHarold (Trey) Watson GowdyHouse Dem moves to force vote on bill protecting Mueller Overnight Regulation: Groups sue over decision to end pay-data rule | EU proposes tax on tech companies | Sessions issues memo on death penalty for drug cases | Pruitt spent 5K on first class flights Overnight Energy: EPA says Pruitt's security detail flies first class | Lackluster offshore drilling sales | Oil companies snag leases near Bears Ears monument MORE (R-S.C.) as well as former South Carolina Attorney General Henry McMaster (R). Scott's name has been the one to receive the most attention.

Haley continued to play coy about a decision on Thursday, posting the lyrics to Adele's "Rumour has it" on her Facebook page without mentioning the seat.

Sources say she will pick a replacement for DeMint soon, though she has given no timeline for a choice. Whoever is chosen will be up for election in 2014, and could face a primary challenge.