Ryan, House Budget Committee chairman and architect of the chamber's controversial budget proposal, said he would prefer to stay in where he is, The Hill reported.
"I am grateful for the tremendous outpouring of encouragement that I have received from my friends and supporters since Senator Kohl announced he would not seek re-election to the U.S. Senate," Ryan said in a statement. "For my family and me, the most important factor in making this decision was determining where I could make the biggest difference."
Democrats have used Ryan's budget, especially its proposed sweeping reforms to Medicare and Medicaid, as a club against Republicans.
Kohl announced Friday he won't seek a fifth term.
Republican Tommy Thompson, the former Wisconsin governor and President George W. Bush's first Health and Human Services secretary, told friends he plans to run for Kohl's seat, sources in Wisconsin told Politico.
Names mentioned as possible Democratic candidates include Russ Feingold, who lost his re-election bid last year to Sen. Ron Johnson, Milwaukee mayor Tom Barrett, and Reps. Tammy Baldwin and Ron Kind.
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