Hillary Clinton’s campaign is vetting James G. Stavridis, a retired four-star Navy admiral who served as the 16th supreme allied commander at NATO, as a possible running mate, according to a person with knowledge of the vetting process.

Some close to Mrs. Clinton, the former secretary of state, say she was always likely to have someone with military experience on her vice-presidential shortlist, and Mr. Stavridis, currently the dean of the Fletcher School at Tufts University, fits the description.

During his four years as NATO’s supreme allied commander, he oversaw operations in the Middle East — Afghanistan, Libya and Syria — as well as in the Balkans and piracy off the coast of Africa.

The Clinton campaign declined requests for comment, and Mr. Stavridis declined to comment other than referring calls to the campaign. The person with knowledge of the vetting spoke anonymously because of the sensitive nature of the process.