Sen. John CornynJohn CornynSenators struggle to get spending bills off ground as shutdown looms The 13 Republicans needed to pass gun-control legislation The Hill's Morning Report — Biden steadies in third debate as top tier remains the same 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 AlexanderAndrew (Lamar) Lamar Alexander The 13 Republicans needed to pass gun-control legislation Liberal group urges Senate panel to vote against Scalia as Labor secretary Suburban anxiety drives GOP on guns MORE (Tenn.), currently the third-ranking Senate Republican, and other possible candidates, including Sen. John ThuneJohn Randolph ThuneTrump, lawmakers consider app that would conduct background checks: report 'Mike Pounce' trends on Twitter after Trump slip at GOP retreat The Hill's Morning Report — Biden steadies in third debate as top tier remains the same 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 BarrassoHouse votes to block drilling in Arctic refuge Lobbying World Meet the Democratic senator trying to negotiate gun control with Trump 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.