The Mazzeh airbase houses Syrian Air Force intelligence, and in early 2017 the Syrian regime accused its neighbour Israel of bombing the base.
The leaders of Iran, Turkey, and Russian Federation are expected to meet in Iran this week to discuss the situation in Syria.
The Israeli government does not comment on the details of its military operations overseas, but it has claimed it had hit Iranian forces on Syrian soil.
Jeffrey and Rayburn would travel on to Jordan and Turkey, where they would reiterate the USA position against a military offensive in Idlib, the State Department said.
The report of the attack came at a time when Iranian Foreign Minister Mohammad Javad Zarif was visiting Damascus for talks with senior Syrian officials, in advance of the battle for Idlib in the northwest of the country, which is considered the last major rebel enclave.
"And the remaining terrorists in the remaining parts of Idlib must be cleaned out and the region should be placed back under the control of the Syrian people".
Zarif said it was necessary to consult "with our Syrian friends" ahead of the September 7 summit, according to Fars.
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Iranian President Hassan Rouhani is scheduled to meet Russian President Vladimir Putin and Turkish President Tayyip Erdogan in Iran, according to Fars News.
In their meeting Monday, Assad and Zarif also discussed what they called "western pressure" on their two countries, in apparent reference to the USA sanctions on Iran and calls for limiting Iran's role in Syria.
"Syria's territorial integrity should be safeguarded and all tribes and groups, as one society, should start the reconstruction process, and the refugees should return to their homes", Zarif said.
Zarif's visit on Monday comes after Amar Hatami, Iran's defence minister, travelled to Damascus and signed an agreement for defence cooperation with his Syrian counterpart Ali Abdullah Ayoub.
Iranian Foreign Ministry spokesman Bahram Qassemi told reporters in Tehran that Syria has every right to reclaim its territory from terrorists and Iran's support will continue.
Tahrir al-Sham, which includes the al Qaeda-linked group formerly known as Nusra Front, is the most powerful jihadist alliance in Idlib.
Assad's government has long referred to any opposition fighters as "terrorists". He said it is not possible to tolerate the situation there indefinitely, according to Interfax.