The jury selection process will enter its third day in Manhattan federal court.
U.S. District Judge Sidney Stein said on Tuesday that a jury could be empaneled by Wednesday after prosecutors and defense lawyers exercise challenges to seating various jurors. Opening statements would follow.
Menendez, 70, a Democrat, has pleaded not guilty to 16 criminal charges including bribery, fraud, acting as a foreign agent and obstruction. He is being tried alongside New Jersey businessmen Wael Hana and Fred Daibes.
The senator's wife Nadine Menendez, 57, is scheduled to be tried on July 8, with the delay resulting from what her lawyers called a serious medical condition.
All have pleaded not guilty. The bribery trial is Robert Menendez's second, with the first ending in 2017 in a mistrial after jurors deadlocked.
Prosecutors are expected to detail a complex and sordid array of corruption that they say lasted from 2018 to 2023.
The Menendezes are accused of accepting hundreds of thousands of dollars in bribes from Hana, Daibes and insurance broker Jose Uribe, in exchange for the senator providing political favors and aid to the governments of Egypt and Qatar.
Prosecutors said the senator promised to help Egypt obtain arms sales and other aid.
Mendez also helped Hana obtain a lucrative monopoly on certifying that meat exports to Egypt conformed to Islamic law, and tried to help Daibes secure millions of dollars from a Qatari investment fund, the prosecutors added.
Menendez also allegedly tried to interfere in a federal criminal case against Daibes in New Jersey, and in state criminal cases involving two of Uribe's associates.
Prosecutors said FBI agents found more than $480,000 of cash in the Menendezes' home, much stashed in clothing, closets and a safe.
Bribes also included more than $100,000 in gold bars, and a $60,000 Mercedes-Benz convertible, prosecutors said.