WASHINGTON — President-elect Donald J. Trump is expected to choose as director of national intelligence two-time Senator Dan Coats, a former ambassador to Germany, secret foodie and lover of all things Indiana who also served as a member of his chamber’s Intelligence Committee.

Known for a self-effacing style, Mr. Coats was popular among his colleagues. “I always thought he should wear a red cardigan,” said Senator Cory Gardner, Republican of Colorado. “He was the closest thing to Mister Rogers we could come up with.”

While fiscally conservative, Mr. Coats, an Indiana Republican who completed his second Senate stint this month, often found common cause with Democrats, who described him as thoughtful on intelligence and national security issues, with a sharp intellect and disarming humor.

“I have always been impressed with his demeanor,” said Senator Angus King, a Maine independent who caucuses with the Democrats, and who served on the Intelligence Committee with Mr. Coats and traveled with him in Eastern Europe. “He’s not a fierce partisan and knows the intelligence community. He’s very amiable and easy to work with.”