Manama is the third leg of the tour that has already taken in Jerusalem and Khartoum. It is due to end in the United Arab Emirates, which earlier this month became only the third Arab country to agree to normalise relations with the Jewish state.
Pompeo has said he is hopeful other nations will follow suit, despite criticism of the deal from some parts of the Arab world.
The Palestinian leadership has derided the UAE's move as a "stab in the back".
Sudan on Tuesday also dashed US hopes for a speedy breakthrough, saying its transitional government, which replaced ousted strongman Omar al-Bashir last year and is set to rule until elections in 2022, has "no mandate" to take such a weighty step.
Manama, whose contacts with Israel date back to the 1990s, was the first Gulf country to welcome the UAE move and is considered a front-runner to follow in its footsteps.
Like most Gulf countries, Bahrain shares with the Jewish state a common enemy in Iran, which Manama accuses of instigating protests by the nation's Shiite Muslim community against the ruling Sunni Al-Khalifa dynasty.
Bahrain -- a close ally of regional heavyweight Saudi Arabia -- is unlikely to establish official relations with Israel without Riyadh's blessing, but it could play an important intermediary role.
"While Saudi Arabia cannot directly normalise relations amid a stalemate in the peace process, Bahrain could become a hub for Saudi-Israeli exchange," Andreas Krieg of King's College London told AFP.
Saudi Arabia, while not condemning the UAE-Israel deal, has refused to normalise ties until Israel signs an internationally recognised peace accord with the Palestinians.
Not only would a formal recognition of Israel be seen by Palestinians and their supporters as a betrayal of their cause, it could also hurt the kingdom's image as the leader of the Islamic world.
While in Bahrain, Pompeo will meet Bahrain's Crown Prince Salman bin Hamad Al-Khalifa before talks with UAE Foreign Minister Abdullah bin Zayed Al-Nahyan on the next leg of the tour.
On Tuesday, the US chief diplomat spoke by phone with Abu Dhabi's Crown Prince Sheikh Mohammed bin Zayed Al-Nahyan, who is seen as the driving force behind the Israel agreement.
The two discussed the historic deal "and the prospects for strengthening it in a way that serves the foundations of peace and stability in the region", the official Emirati news agency WAM said.
Israeli Prime Minister Benjamin Netanyahu has denied reports that the UAE deal hinges on the sale of US F-35 stealth fighter-jets to the Emirates, saying he opposes a move that could reduce Israel's strategic edge in the region.
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