Prince Faisal bin Farhan, the Saudi foreign minister, denied on Twitter that the Sunday night clandestine meeting took place at all.
But Israeli media, citing unnamed officials and pointing to flight radar data, claimed that Mr Netanyahu and his spy chief, Yossi Cohen, had flown by business jet to the Saudi megacity of Neom to meet Crown Prince Mohammed bin Salman and Mr Pompeo, who was also visiting.
Senior Arab diplomats were quoted by Israeli public broadcaster Kan radio as saying that the Saudis “wanted to expand their cooperation with Israel in order to address the threat posed by Iran but that they were still cautiously considering the issue of normalising relations”.
If true, it would have been the first publicly acknowledged visit of an Israeli premier to the ultraconservative kingdom that is the birthplace of Islam and has historically championed the Palestinian cause.
People travelling with Mr Pompeo declined to comment, and Mr Netanyahu, in a meeting with his Likud party, also declined to confirm the visit.
As speculation whirled, Prince Farhan later said on Twitter: “No such meeting occurred. The only officials present were American and Saudi.”
However, on Tuesday both public radio and Israel’s Channel 12 cited unnamed officials confirming the visit, adding that Mr Netanyahu and Mr Pompeo’s “hopes were frustrated”.
“Despite the efforts by Netanyahu and Pompeo to convince them, the Saudis made clear that, at the moment, they are not ready to take the extra step. That’s why no additional [normalisation] ceremony can be expected in the near future,” an official told Channel 12.
Kan radio, meanwhile, cited an official as saying: “No breakthrough toward an agreement is expected. It won’t happen so fast.”
Over the past few months the United Arab Emirates and Bahrain have signed US-brokered diplomatic deals with Israel, in a major foreign policy win for Donald Trump.
The US president had, at the time, suggested that Riyadh would soon follow suit, delivering him yet another diplomatic victory.
But all reports of an impending deal have been denied by the kingdom.
For years Gulf Arab states have shunned direct relations with Israel over the treatment of the Palestinians.
Saudi Arabia has spearheaded many peace initiatives including one in the early 2000s that offered the normalisation of Gulf ties with Israel if an independent Palestinian state was created and Israel withdrew from territory captured in the 1967 war.
But over the years, Israel is known to have opened clandestine channels of communication with Arab states, largely over military technology sales and regional issues including a mutual enmity towards Iran.
There was speculation in Israeli media that the Trump administration was pushing for a Saudi-Israel deal before he leaves office in January and Joe Biden takes over.
In another potential blow for Mr Trump, Israeli media, citing western diplomats, reported on Tuesday that the Palestinian leadership has come to an understanding with the Biden transition team through intermediaries.
The Palestinian leadership cut all diplomatic ties with the Trump administration in 2017 when Washington recognised the contested city of Jerusalem as Israel’s capital. Mr Trump later slashed all aid to the Palestinians and oversaw the drafting of a peace deal which has been labelled the most pro-Israel vision of the region post-conflict.