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Others on Haley's list include Reps. Tim ScottTimothy (Tim) Eugene ScottSenate GOP urges Trump administration to work closely with Congress on NAFTA Fed nominees vow to rebuff pressure from Trump on interest rates The Hill's 12:30 Report MORE (R-S.C.) and Trey GowdyHarold (Trey) Watson GowdyWhite House lawyer’s presence at FBI meetings sets off alarm bells for Dems Dems after briefing: 'No evidence' spy placed in Trump campaign House GOP sets three FBI interviews in Clinton probe 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.