Coleman, who narrowly lost to Franken in 2008, would have likely been the GOP's strongest chance to unseat the first-term senator. He immediately touted both Rep. Erik Paulsen (R-Minn.), who hasn't ruled out a bid, and Rep. John Kline (R-Minn.) as strong potential contenders for the seat.

"Franken has been invisible, not just nationally, but in Minnesota. Cong. Paulsen or Kline would make this a competitive race in a moment," he tweeted. "I'm confident a strong candidate will emerge against Al."

The former senator has stayed involved in national politics, running the center-right super PAC American Action Network and helping with the Hispanic Leadership Network, a group looking to help expand Hispanics' presence in the GOP.

Those close to Coleman told The Hill in November that he was unlikely to run against Franken but might make a bid for Minnesota governor — and his next tweet hinted that might be a possibility.

"My hope is 2 be spending more time focused on Minnesota, not as much on Washington," he wrote.