Former Wisconsin Gov. Tommy Thompson (R), a cabinet member in the George W. Bush administration, intends to run for Senate next year, while Rep. Paul Ryan (R) is passing on the open-seat contest.

Ryan, the House Budget chairman, is set to make his intentions public on Tuesday and several news outlets reported that he will not run for the seat being vacated by the retiring Sen. Herb Kohl (D).

Thompson’s thinking, confirmed this morning by a GOP consultant in touch with the Thompson camp, could signal a significant recruiting victory for Republicans, although the former governor is unlikely to have a clear primary.

Democrats have wasted little time in trying to dirty up the former Health and Human Services secretary, suggesting they believe he may be the man to beat as the field comes together in the wake of Kohl’s announcement.

A Democratic campaign strategist describes Thompson as a perennial candidate who has “entertained” running for office four times since 2006, including a run for the presidency in 2008.

“Also, he enthusiastically endorsed Obama’s health care bill and refused to endorse [Gov. Scott] Walker’s collective bargaining bill,” said the strategist. “I’m sure national Republicans would take the Packers towel boy over this guy.”

The Hotline first reported over the weekend that Thompson was considering jumping into the Senate race.