Schweitzer said he'd leave the decision to Gov. Steve Bullock (D) if Baucus is confirmed as U.S. ambassador to China.
Speculation has centered on Bullock picking Montana Lt. Gov. John Walsh (D). Walsh is already running for Baucus's seat, and might have a better chance of winning if he was running as a sitting senator.
Schweitzer's former lieutenant governor, John Bohlinger (D), however, is challenging Walsh in a primary.
Bohlinger's campaign has called on Bullock to nominate a caretaker for the seat rather than hand it to Walsh and boost his electoral chances.
Schweitzer wouldn't say whether he agreed with his former running mate.
Asked if he would have picked a caretaker, he said: "I'm not governor, that's hypothetical. I'll support Steve Bullock's decision."
He also refused to say if he'd talked to Bullock in recent days.
"I may have, I may not have," he said.
He also declined to comment on whether he thinks Baucus would make a good ambassador before rushing off the phone. Schweitzer and Baucus have had a sometimes-tense relationship in the past.
Schweitzer had considered running for Baucus's Senate seat earlier this year. He's also hinted at a potential presidential run in 2016.
Bullock hasn't said who he'll appoint to replace Baucus, who was formally nominated by President Obama on Friday.
Bullock's statement following Obama's nomination praised Baucus but didn't comment on how he'll approach the nomination.
“Max has dedicated his life to public service and the notion that, through hard work, he could make Montana an even greater place — something I first got to see as a high school student visiting his office," Bullock said in a statement.
"From helping create the Children's Health Insurance Program to beating back attempts to privatize Social Security, Max has always put Montanans first. I thank him for his service to our state and wish him the best of luck with his new responsibility, representing our country overseas."