Minnesota Gov. Mark Dayton does not plan to get ahead of Franken's scheduled announcement Thursday, a senior Minnesota Democrat close to Dayton told CNN, but the governor's "expectation and hope is for Franken to resign."
Should Franken step down, top names to replace him are Democratic Reps. Keith Ellison and Tim Walz, this official said. Another leading contender will be Lt. Gov. Tina Smith, a former chief of staff to Dayton.
"Don't overlook Lt. Governor Smith," the official said. "She could be the perfect choice."
Dayton, a former US senator, might also tap his former colleagues for advice in his pick, including Senate Minority Leader Chuck Schumer. "There will be an open line of communication," said the senior Democratic strategist.
The field of Democrats looking to succeed Dayton as governor might also be ripe for picking to fill Franken's seat. Attorney General Lori Swanson would be a particularly attractive candidate, said one senior Democratic strategist.
Come the 2018 midterm elections, the Senate seat would be up for grabs -- and would likely become a target for the Republican Party.
Republicans weighing a bid for governor could decide to look to the Senate instead, including Minnesota State House Speaker Kurt Daudt.
Former Gov. Tim Pawlenty, also a former candidate for president, would also likely have the resources and connections to mount a serious campaign. Another GOP former presidential candidate, former Rep. Michele Bachmann, could also leverage her national profile to run for Senate.
Pawlenty has been weighing a bid for governor and has kept an active profile in Minnesota.
"Given his interest in foreign policy and federal policy, the Senate would be a great fit," said one Republican strategist who knows Pawlenty.
Among the Minnesota congressional delegation, Rep. Tom Emmer, who ran for governor in 2010, would be a potential GOP candidate to watch, said one GOP campaign strategist. Rep. Erik Paulsen is also viewed by Republicans as someone who is ambitious and well-regarded, and might be a natural Senate candidate, another Republican strategist added.
But GOP members of Congress, like Emmer and Paulsen, might be hesitant to run for Senate in 2018, an election year that strategists widely predict will be a challenging one for Republicans.
"I can't see any one of them making the jump in a cycle like this," said the second Republican strategist.
Correction: Gov. Dayton may consult Senate Minority Leader Chuck Schumer about replacing Franken. An earlier version misstated the person with whom he might consult.