Florida House Speaker Dean Cannon told CNN Tuesday a state commission is likely to choose that date on Friday.
The move would violate Republican National Committee rules that bar any state other than the first four "carve-out" states -- Iowa, New Hampshire, Nevada and South Carolina -- from having a primary before March 6.
Those four states would likely move up their dates so they could preserve their early-voting status, and other states would likely reschedule to preserve their influence, CNN said.
"If Florida decides to go in January, they blow the RNC planned calendar wide open and we'll be back to campaigning over the holidays as Iowa and New Hampshire hold their presidential caucus and primary in early January," said Michigan RNC member Saul Anuzis, who is on the committee's presidential nominating schedule committee.
States that violate the RNC rules could lose half their delegates, who will choose the nominee at the RNC convention in Tampa in August.
States must submit dates for their primary and caucuses to the RNC by Saturday.
RNC Chairman Reince Priebus and other GOP officials have been trying to persuade Florida Gov. Rick Scott and state lawmakers to move the primary to Feb. 21, sources told CNN. But even if the state settled on that date, it would lose half its delegates.
The New York Times reports one senior GOP official said the scramble for position among several states has been "like playing a game of Jenga -- you move one state, and the whole thing falls down."