Franken said he would step down "in the coming weeks" after a series of sexual misconduct allegations caused support in his own party to collapse. Democratic Gov. Mark Dayton will appoint a replacement to serve until next year's election.
Franken's departure is a headache for Democrats, exposing another seat in a midterm election that already had them defending two dozen incumbents.
Republicans are eager to recapture a seat that Franken won in 2008 by a tiny margin and only after a monthslong recount. They're also hoping the sexual harassment scandal that engulfed Franken will saddle Democrats with enough baggage to help Republicans break through in 2018.
"A lot of the electoral momentum recently has been with Democrats, and I think Franken's resignation will provide a strong boost for Republicans in Minnesota in 2018," said Brian McClung, a former aide and longtime adviser to Pawlenty.
Republicans haven't won statewide in Minnesota since Pawlenty won a second term as governor in 2006. But GOP operatives see a positive sign in President Donald Trump's narrow loss in 2016 - by just 1.5 percentage points - in a state that hasn't gone Republican in the presidential race in generations.
"I think this adds one more competitive seat to the mix," Colorado Sen. Cory Gardner, who is running the GOP's Senate election efforts, said.
Former Sen. Norm Coleman, who served one term before losing to Franken, quickly announced he would not run in 2018, but other candidates could emerge.
Pawlenty had eyed the U.S. Senate the year Coleman won: He was minutes away from announcing a campaign in 2002 when a call from then-Vice President Dick Cheney persuaded him not to challenge Coleman. The former two-term governor has been weighing a return to elected office since a failed presidential bid in 2012, a year after he left the governor's office.
Pawlenty has been CEO of the Financial Services Roundtable for five years, after not seeking a third term as governor and trying unsuccessfully for the 2012 Republican presidential nomination. The position with the leading financial services lobbying group in Washington has kept him close to national tax and monetary policy, including the GOP-controlled Congress' tax plans this year.
"He's always had an interest in the Senate, so there's every reason to believe that conversation will be refreshed," former Coleman aide Josh Holmes said. Holmes is also a former aide to Senate Majority Leader Mitch McConnell, who is largely responsible for candidate recruiting in his drive to retain a majority.
Pawlenty did not return calls seeking comment.
Other Republicans who may consider running include State House Speaker Kurt Daudt, who has been considering seeking the governor's office, and Rep. Tom Emmer, who represents the state's most conservative congressional district and narrowly lost to Dayton in 2010 before going on to win a House seat.
On the Democratic side, Franken's departure adds to the strain for a party trying to cut into the GOP's two-seat margin in the Senate while having to defend many more seats.
Ten Democratic senators are seeking re-election in states Trump carried last year. Robust Republican primary campaigns are already underway in several, including in Indiana, Missouri, Montana, Pennsylvania, West Virginia and Wisconsin. Democrats are defending 23 seats overall, while the GOP is defending nine. Two independents who caucus with Democrats also face re-election.
Democrats' hopes in Minnesota could ride on someone shifting out of next year's race for governor. A handful of top candidates - U.S. Rep. Tim Walz, state Rep. Erin Murphy and St. Paul Mayor Chris Coleman - have spent months connecting with party activists and their donors would be critical in a costly election.
Dayton's appointment could give someone a running start for a 2018 campaign, but the governor may also choose to simply make a short-term replacement, tapping someone who doesn't plan to face voters.
His lieutenant governor, Tina Smith, has been most frequently mentioned for the temporary appointment. She's known largely for behind-the-scenes work, including as Dayton's former chief of staff. She ran former Vice President Walter Mondale's brief Senate campaign in 2002 after Sen. Paul Wellstone died in a plane crash. She also served as a top executive at Planned Parenthood in Minnesota, North Dakota and South Dakota.
But Smith previously announced she wouldn't run for governor next year, suggesting that if she gets the appointment she would be no more than a caretaker.
Dayton could also look to a pair of fellow Democratic statewide elected officials: Attorney General Lori Swanson or State Auditor Rebecca Otto.
Or he might choose to send a loud signal against sexual harassment by picking Rep. Erin Maye Quade, a Democratic state lawmaker who, along with other women, accused two fellow state lawmakers of sexual harassment, resulting in their resignation last month.
Dayton said he would make his appointment "in a couple of days."
Associated Press writers Tom Beaumont in Des Moines, Iowa and Kevin Freking in Washington, D.C., contributed to this report.
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