Barrack, 75, is not charged with acting as a Saudi agent, but the country is close with the UAE.
U.S. intelligence says the murder of Khashoggi, a Saudi insider-turned-critic, was approved by Crown Prince Mohammed bin Salman, the de facto ruler.
The blockade of Qatar by Saudi Arabia, the UAE and others began in 2017.
Prosecutors say that during the blockade, Barrack told Rashid Al Malik - an associate also accused of being an Emirati agent - that the United States was considering hosting a summit to resolve the conflict.
Al Malik, who is at large, then told UAE officials about the possible meeting, prosecutors say.