The US president sees a maintained blockade as the least risky option, according to the anonymous sources.
The idea is to strike at the Iranian regime's finances to force the nuclear capitulation that Tehran has long rejected.
Trump's line is said to have become clear during a meeting in the White House Situation Room on Monday, where he is said to have expressed support for a continued blockade - which is intended to pressure Iran's economy and oil exports by stopping ships to and from the country - instead of resuming bombing.
However, a continued blockade prolongs the conflict that has led to sharply rising prices for fossil fuels and declining support for the president, points out The Wall Street Journal .
The third American option - to quickly end the war - is reportedly seen by Trump as a capitulation that allows Iran to dictate the terms.
During Monday's meeting, Trump reportedly rejected Iran's latest proposal, which reportedly involved reopening the Strait of Hormuz and postponing talks on the country's nuclear energy program until later.
