Former U.S. Surgeon General Richard Carmona says Rep. Gabrielle Giffords’ office has asked him to consider a run for the U.S. Senate seat being vacated next year by Sen. Jon Kyl.

Giffords at one time had been mentioned as a potential candidate for the seat, but her name now seldom surfaces in lists of potential candidates.

She is recovering from a gunshot wound she suffered during a January at a political event in Tucson and hasn’t revealed her future political plans.

Carmona declined to say who in Giffords’ office approached him and said he hasn’t yet decided whether to run for the seat.

The candidates include Rep. Jeff Flake, real estate investor Wil Cardon, general contractor Douglas McKee and former Youngtown Mayor Bryan Hackbarth.

Former Arizona Democratic chairman Don Bivens also is considering a run.