Sen. John CornynJohn CornynHouse passes bill to expedite financial disclosures from judges McConnell leaves GOP in dark on debt ceiling Congress's goal in December: Avoid shutdown and default MORE (Texas) will run to become the next Senate GOP whip, a senior aide to the senator said Friday. 

Cornyn, the chairman of the National Republican Senatorial Committee, has begun reaching out to colleagues to gauge support for his candidacy to replace Sen. Jon Kyl (Ariz.) as the No. 2 Republican in the next Congress. Kyl announced his retirement on Thursday.

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The Texan's candidacy would likely pit him in a race against Sen. Lamar AlexanderLamar AlexanderMcConnell gets GOP wake-up call The Hill's Morning Report - Presented by Alibaba - Democrats return to disappointment on immigration Authorities link ex-Tennessee governor to killing of Jimmy Hoffa associate MORE (Tenn.), currently the third-ranking Senate Republican, and other possible candidates, including Sen. John ThuneJohn Randolph ThuneThe Hill's Morning Report - Presented by Facebook - Congress avoids shutdown Senate dodges initial December crisis with last-minute deal Congress averts shutdown after vaccine mandate fight MORE (S.D.), another member of leadership, who will decide by the end of February whether to run for president in 2012.

Cornyn is currently in charge of efforts to deliver the Senate majority to the GOP in 2012, an undertaking aided by the fact that Democrats have to defend 23 seats in this coming cycle, many in swing or conservative-leaning states.

If Cornyn were to help Republicans win the majority, good will from his 2010 and 2012 efforts atop the campaign committee could help him win the top Senate job.

Cornyn started making calls to colleagues on Thursday, according to an aide, but the senator did not want to announce his intentions lest he appear to try to overshadow Kyl's retirement announcement.

Sen. John BarrassoJohn Anthony BarrassoCongress averts shutdown after vaccine mandate fight Sunday shows - Spotlight shifts to omicron variant Barrasso calls Biden's agenda 'Alice in Wonderland' logic: 'He's the Mad Hatter' MORE (R-Wyo.), the newest member of the Senate GOP leadership, cast the race between Alexander and Cornyn as fairly even so far.

"A couple of folks have already spoken up and I have great confidence in the incredible work done by Sen. Alexander as well as Sen. Cornyn. They are both remarkable members of the current leadership and we're fortunate to have them," he said at CPAC, the gathering of conservatives in Washington this weekend.

On the notion that Cornyn has a leg up on Alexander: "That's a lot of speculation. They're both terrific people," he said of the notion that Cornyn had a leg up on Alexander.

Shane D'Aprile contributed to this post.

Updated at 12:05 p.m.