The declared objective of Tuesday's trip is to discuss Mideast peacemaking.
But Prime Minister Benjamin Netanyahu is also expected to discuss negotiations to swap hundreds of Palestinians imprisoned in Israel for an Israeli soldier captured by Gaza militants in 2006.
Egypt and Germany have been mediating those talks.
Through the mediators, Israel has forwarded its latest proposal to Gaza's Islamic Hamas rulers. They have not responded.
A Netanyahu ally quoted the Israeli leader as telling Cabinet ministers that "it's not clear there will be a deal."
Netanyahu said the deadly shooting of an Israeli settler last week highlighted the risks of a deal.