With Congress’ legislative agenda winding down, K Street lobby shops have begun wooing senior Senate Republican aides to leave the Hill now so the lobbyists-to-be can ride out their one-year bans during the upcoming election year.

Figuring the Senate likely has a better-than-even shot of flipping to GOP control, K Street hiring managers say they have their sights on the chamber’s top aides. And they’d like to bring them on sooner, in many cases, because they want them unfettered to push client matters on the Hill as soon as the 113th Congress convenes.

“Senior-level Senate Republican staffers will be in demand, and it’s a good time to leave now because they can sit out their ban during a period where there will not be a lot of legislative activity,” said Ivan Adler, a K Street recruiter and principal at the McCormick Group.

While operating under a lobbying ban, newly minted K Streeters can still provide behind-the-scenes counsel to clients, and they could easily take part in some of next year’s most notable activities such as fundraising and the presidential nominating conventions. But former top Senate aides are prohibited from lobbying the entire chamber for 12 months.

“There is no doubt that it is smart for firms, depending on their growth needs, to hire into the election. They are gaming it out right now,” said Alex Vogel, a former top Senate aide who is now a partner with Mehlman Vogel Castagnetti. “There is demand, real demand for senior Senate people and leadership folks in particular.”

Some of the names atop K Street’s wish list, downtown sources say, include Rohit Kumar, who is deputy chief of staff to Senate Minority Leader Mitch McConnell (Ky.); McConnell’s leadership office chief of staff, Sharon Soderstrom, who is considered unlikely to decamp for the private sector; Wally Hsueh, minority staff director on the Senate Small Business and Entrepreneurship Committee; Jon Gans, deputy chief of staff and policy director for Senate Minority Whip Jon Kyl (Ariz.); and another senior McConnell leadership aide, John Abegg.

Mark Prater, a senior Finance Committee aide for Sen. Orrin Hatch (Utah) who served as staff director for the Joint Committee on Deficit Reduction, is another potential prospect that hiring managers would like to scoop up. And Matt Sonnesyn, the former chief of staff for Sen. Lamar Alexander (R-Tenn.), is said to be, according to sources, finalizing his future plans. The staffers either declined comment or did not return calls seeking comment.

Vogel and other downtown lobbyists noted that the staffers themselves are probably less concerned about the timing of their cooling-off periods and typically will opt to leave for the private sector based on their own personal or professional timelines.

But Sheila Krumholz, executive director of the nonpartisan Center for Responsive Politics, said many Hill aides keep their K Street prospects in mind.

“If your plan includes K Street, there might be some mutual interest in the timing,” she said. As for the firms, associations and corporate offices looking to make hires, she added that many want to have their teams in place even before next year’s election results come in. And many already made big investments in House-connected Republicans after the 2010 midterms.

“It’s not surprising that firms might be planning ahead and trying to pick out the people they’d like to lure away now so that they’re ready to roll in January 2013,” she said.

Some top K Street executives, though, cautioned that the Hill prospects may confront a relatively down lobby marketplace, even if it is better than the overall economy.

“A lot of the firms are tightening their belts,” one lobby shop owner said. But he added that in-house corporate shops “can afford to pick up a senior staffer and let them cool for a year.”

Adler said the senior Senate aides aren’t likely to find any problems fielding top salaries from K Street employers of any type.

“I don’t think their compensation will be negatively affected by the economy,” he said. “Political Washington is in another parallel when it comes to compensation.”