Baucus elaborated in a follow-up statement sent to The Hill.

"My mentor Mike Mansfield once told me, ‘Max, when you serve, you serve to the hilt and when you're done, you're done,’" he said in the statement.

"Right now, I'm focused on working hard for the people of Montana for the next year and a half, and when I’m gone it will be up to the people of Montana to decide who is next. If Brian decides to run, he will be a good candidate and a good Senator. The ultimate decision is up to the people of Montana."

A Baucus spokesman said that "there's been no bigger supporter" of the Montana Democratic Party than Baucus and promised the senator will "continue to be looking for ways to support the DSCC, the Montana party, Montana Democratic candidates and causes as he always has."

A source familiar with Baucus's donation told the The Hill the Montana senator "has consistently been among the very top contributors to the DSCC, and today's move signals that he's continuing to be a top supporter of Senate Democrats after announcing that he won’t run again.

The source noted that Baucus had given more than half a million dollars to the Democratic committee last year alone. Baucus's campaign had $4.8 million cash on hand as of the end of March, shortly before he announced his retirement.