WASHINGTON—The Trump administration is considering a significant expansion of the U.S. military footprint in the Middle East to counter Iran, including dozens more ships, other military hardware and as many as 14,000 additional troops, U.S. officials said.

The deployment could double the number of U.S. military personnel who have been sent to the region since the start of a troop buildup in May. President Trump is expected to make a decision on the new deployments as soon as this month, those officials said.

Mr....