Senator Tom Cotton of Arkansas has unexpectedly emerged as a top contender to become Donald J. Trump’s running mate, a signal that the former president is heavily weighing experience and the ability to run a disciplined campaign over other factors.

Mr. Cotton’s ascendance comes as Mr. Trump’s leading vice-presidential options have increasingly come into focus, according to three people with direct knowledge of Mr. Trump’s thinking who insisted on anonymity to discuss private meetings.

These people said that Mr. Trump’s other current favorites were Gov. Doug Burgum of North Dakota and three of Mr. Cotton’s Senate colleagues: Marco Rubio of Florida, Tim Scott of South Carolina and J.D. Vance of Ohio. The former president has also discussed the five Republican men as potential candidates for administration posts if he were to unseat President Biden in November.

Still, the people close to Mr. Trump cautioned that his vice-presidential preferences might change.

Taken together, the current list of top contenders reflects his desire to choose a running mate who would carry relatively little risk of creating unwanted distractions for a presidential campaign already facing multiple legal threats.

Mr. Trump’s interest in Mr. Cotton, who won a second term in the Senate in 2020, reflects this do-no-harm mentality.

The former president has said privately that he views Mr. Cotton as a reliable and effective communicator in cable news interviews. Mr. Trump has also praised Mr. Cotton’s Army service, which included deployments to Iraq and Afghanistan, and the fact that he is a fellow Ivy League graduate. Mr. Trump went to the University of Pennsylvania, and Mr. Cotton attended Harvard, earning undergraduate and law degrees.