May 25, 2017 0447 GMT
Sources told Axios news website that Adelson was unhappy about Tillerson's statement he made on Sunday in which he said President Donald Trump was being “very careful” in weighing his campaign promise to move the embassy.
During the election campaign, Trump had vowed to move the US embassy immediately after assuming office, but Tillerson poured cold water on Israeli hopes.
"As you know, the president has recently expressed his view that he wants to put a lot of effort into seeing if we cannot advance a peace initiative between Israel and Palestine," Tillerson said.
"And so I think in large measure the president is being very careful to understand how such a decision would impact a peace process,” he stated.
Last year, speaking at the pro-Israel lobby American Israel Public Affairs Committee (AIPAC), Trump announced that the US "will move the American embassy to the eternal capital of the Jewish people, Jerusalem."
Since then, Adelson has been closely following up on whether Trump keeps his campaign pledges regarding Israel, according to reports.
Adelson is the CEO of the Las Vegas Sands casino group, the largest casino company in America. He was listed by Forbes in August 2016 as having a fortune of $33.2 billion, making him the 12th richest person in the world.
He is a major contributor to Republican Party candidates, which has resulted in his gaining significant influence within the party.
Adelson, a Zionist Jew, has said his most important issue when considering which candidates to support in US elections is “the safety of Israel.”
He had previously expressed interest in Florida Senator Marco Rubio and his wife Miriam liked Texas Senator Ted Cruz.
Adelson and his wife spent tens of millions of dollars in the 2016 presidential campaign cycle.