"Full normalisation between Israel and Saudi Arabia is a stated goal of the administration," Sullivan said, according to Israeli broadcaster Kan.
"I am not going to say anything further lest I upset the efforts we are undertaking on this issue," Sullivan added.
Meanwhile, the head of Israel's national security council, Tzachi Hanegbi, told Israeli channel Reshet 13 News: "We are very, very hopeful that there will be a breakthrough during his visit."
Hanegbi spoke this week with his counterpart Sullivan, who on Saturday is set to travel to Saudi Arabia.
Sullivan will likely meet with Saudi Crown Prince Mohammed bin Salman, Hanegbi said.
Israel has sought normalisation with Arab states in a bid to strengthen its position in the region and expand economic opportunities, including weapons sales.
Israeli Prime Minister Benjamin Netanyahu had publicly expressed hope of normalising relations with Saudi Arabia as part of a regional alliance with Arab states against Iran.
Saudi Arabia - a key player in the region and host of Islam's two holiest sites - has repeatedly said normalisation will not happen until a Palestinian state is created.
Israel illegally occupies East Jerusalem and annexed the entirety of the city in 1980. It maintains a brutal occupation of the West Bank and a siege against the Gaza Strip.
Israel has, however, normalised diplomatic ties with several Arab states since 2020, including Saudi Arabia's neighbours the United Arab Emirates and Bahrain, although most countries in the MENA region do not have ties with it.
Normalisation is highly controversial and is viewed by Palestinians as a betrayal of their national cause.