EAGAN, Minn. — It was four years ago this summer, when Tim Pawlenty ranked high on the list of John McCain’s potential running mates, and Mr. Pawlenty and his wife, Mary, were plowing through a voluminous questionnaire probing deep into their finances and almost every other aspect of their lives.

“I remember the two of us joking one night at some inhumane hour, ‘No way is Mitt Romney doing this by himself!’ ” Mr. Pawlenty later wrote in his book. “We had a good laugh over that.”

After a short-lived presidential bid of his own last year, Mr. Pawlenty is again being considered for the Republican ticket. His fate is in the hands of Mr. Romney, a rival-turned-friend, who is on the cusp of announcing his vice-presidential selection. Mr. Romney has reached a decision, his friends believe, and he may disclose it as soon as this week.