Silman's expected trip to Saudi Arabia follows to recent visits made by Communications Minister Shlomo Karhi and Tourism Minister Haim Katz.
Commanders for Israel's Security endorsed a call by 20 US Senators for any deal between Israel and the Saudis to be conditioned on the Palestinians.
Benny Gantz's trip to the US was very low-profile and comes as Israel and Saudi Arabia move steadily closer to a normalization deal.
Spokespeople for the White House have denied the possibility of any secret visit to discuss Saudi-Israel normalization.
An agreement with the Arab world’s most important state, which also plays a central role in the Islamic world, could serve as an impetus for other Arab and Muslim countries to follow its lead.
Israelis divided on Prime Minister Benjamin Netanyahu's standing amid Saudi peace as New Israeli Voice Index focuses on Middle East peace.
US official John Kirby warned that "as in other complex arrangements, such as this will inevitably be, everyone must make concessions."
Washington could also sweeten any deal by designating Saudi Arabia a Major Non-NATO Ally, a status already given to Israel, the US source said.
Regional sources say that Saudi Arabia will proceed with normalizing relations with Israel regardless of Palestinian opposition.
The Israeli-Palestinian conflict seems to loom over the negotiations for a Saudi-Israeli normalization deal.