Former U.S. Surgeon General Richard Carmona told the Associated Press that members of Rep. Gabrielle Giffords’ (D-Ariz.) political team have asked him to consider running for Senate.

A Democratic source confirmed to Roll Call that Carmona has been meeting with Giffords media consultant, Jason Ralston, for weeks. Their most recent meeting last week took place at Carmona’s Canyon Ranch office and included former Giffords campaign manager Rodd McLeod.

McLeod had been serving as the Congresswoman’s interim district director since Giffords was shot in the head in January in an assassination attempt.

To date, Carmona is the most prominent name on the Democratic side to be considering a run for retiring Sen. Jon Kyl’s (R) seat. While Giffords was viewed as a likely Senate candidate before the shooting, it has been expected for months that Giffords will seek re-election to the 8th district if she runs for anything in 2012.

On the Republican side, Rep. Jeff Flake is the frontrunner for the nomination, although wealthy business investor Wil Cardon and a couple of others are also running.