Israel's Kan public radio and Army Radio reported about the trip on Monday.
If confirmed, it would be the first publicly acknowledged trip by an Israeli leader to ultra-conservative Saudi Arabia.
As US President Donald Trump's term winds down, Pompeo has been trying to coax the Persian Gulf powerhouse to follow its neighbors, the United Arab Emirates and Bahrain, in establishing formal relations with Israel.
Netanyahu's office and the US Embassy in Jerusalem al-Quds had no immediate comment on the reports.
Saudi state media made no mention of any visit by Netanyahu, and the Saudi government's media office did not immediately respond to Reuters queries.
Netanyahu was joined on his Saudi trip by Mossad director Joseph (Yossi) Cohen, who has spearheaded discreet diplomatic outreach to Persian Gulf Arab states, said the Israeli media reports, quoting unidentified Israeli officials.
Riyadh has so far declined to normalize ties with Israel. But since August it has allowed Israeli airliners to overfly Saudi territory to newly available Persian Gulf destinations and Asia.
Avi Scharf of Israel's Haaretz newspaper published aviation tracking data showing that a business jet had made a brief trip from Tel Aviv to Neom, on Saudi Arabia's Red Sea coast, where bin Salman and Pompeo had a scheduled meeting on Sunday.
More publicly closing ranks with the Saudi crown prince could help the conservative Netanyahu burnish his statesman credentials as he faces domestic challenges, including a trial on corruption charges, which he denies, and a feud with centrist coalition partner Benny Gantz, Israel's defense minister.
"Gantz does politics while the prime minister makes peace," Netanyahu spokesman Topaz Luk tweeted.
Asked on Saturday whether Riyadh had changed its position on Israel, Saudi Arabia's foreign minister said the kingdom had supported complete normalization of ties "for a long time", but on condition that Israel and the Palestinians reach "a permanent and full peace deal".