It has instead limited military contacts with Moscow to basic air safety, holding a third round of talks on Wednesday.
The Pentagon said in a short statement that the secure-video conference with Russian defense officials had led to progress in discussions aimed at promoting safe air operations over Syria. It offered no further details.
The U.S. official, who spoke to Reuters on condition of anonymity, said the memorandum of understanding could be implemented in the near future, after follow-on review.
U.S. proposals, first outlined during a secure video conference between the U.S. and Russian militaries on Oct. 1, include maintaining a safe distance between U.S. and Russian aircraft and using common radio frequencies for distress calls.
The U.S. military says Russian aircraft have repeatedly broken air patrols and come close to unmanned, American drone aircraft. The Pentagon on Tuesday also disclosed that U.S. and Russian aircraft came within visual identification range on Saturday.
Russia's state ITAR-TASS news agency quoted the defense ministry on Wednesday as saying the Russian SU-30CM jet was within 2-3 km of the U.S. plane, but came close to identify it, "not to scare it."
U.S. Defense Secretary Ash Carter slammed Russia on Wednesday for what he called "unprofessional behavior."
Carter said Russia's support for Assad showed it was not serious about fighting Islamic State and that Moscow's actions would fan the war.
"We have not, for our part, and will not agree, to cooperate with Russia as long as they continue to pursue a misguided strategy," Carter told a gathering of U.S. Army leaders in Washington.
Russian Foreign Minister Sergei Lavrov said the United States had declined to send a high-level military delegation to Moscow to discuss deeper coordination in fighting in Syria, as had been proposed by Moscow.