The Tennessee Republican also announced he will support Sen. Jon Kyl of Arizona in his bid for Senate minority whip, The Hill newspaper reported Tuesday.
Although Alexander is the first to announce he is running for Republican Conference chairman, the newspaper reports Sens. Kay Bailey Hutchison of Texas and Richard Burr of North Carolina also are considering a run.
Alexander reportedly began soliciting support for his run Sunday, the day before Sen. Trent Lott, R-Miss., announced his resignation, opening up the No. 2 GOP leadership slot for Kyl.
"I have telephoned Jon Kyl to tell him I will vote for him as Trent's successor as whip," Alexander said in a statement Monday. "If Jon is elected, I will be a candidate to succeed him as chairman of the Republican Conference."
2014: The Year in Music [PHOTOS]