Republican Rep. Jeff Flake’s campaign for the Senate seat held by Minority Whip Jon Kyl (R) moved ahead this week, while several Republicans and Democrats continued to examine whether to jump into the Arizona race.

Flake picked up the endorsement of House Budget Chairman Paul Ryan (R-Wis.) on Thursday. The Club for Growth has also endorsed the Arizona Republican, throwing its weight behind him just minutes after Kyl’s decision not to run for re-election in 2012 was confirmed Feb. 10.

Flake’s campaign released an Internet advertisement this week to introduce his candidacy, which was announced Monday.

Among the Republicans recently floated as possible competition for Flake is businessman Tucker Quayle, the older brother of Rep. Ben Quayle (R-Ariz.) and son of Dan Quayle, the former Senator and vice president. On the Democratic side, some are mentioning state Rep. Chad Campbell.

Sources based in Arizona said there is growing speculation that Homeland Security Secretary Janet Napolitano would opt against running. Napolitano previously served as Arizona governor and state attorney general. Napolitano’s press office at Homeland Security had yet to comment on the secretary’s plans Thursday afternoon.