They were expected to be sent to Russia within hours, and U.S. District Judge Kimba Wood announced that the Russian government would release four people to the United States in exchange.
The 10 spy suspects were officially charged on Wednesday. An 11th suspect, who jumped bail last week after being arrested in Cyprus, remains on the loose.
New York Journalist Vicky Pelaez is among those behind bars in the U.S.
"As far as I know, she would have absolutely no desire to go to Russia," said her lawyer John Rodriguez.
Igor Sutyagin, a Russian arms control analyst serving a 14-year sentenced for spying for the United States, had told his relatives he was going to be one of 11 convicted spies in Russia who would be freed in exchange for 11 people charged in the United States with being Russian agents. They said he was going to be sent to Vienna, then London.
In Moscow, his lawyer, Anna Stavitskaya, said a journalist called Igor Sutyagin's family to inform them that Sutyagin was seen walking off a plane in Vienna on Thursday. However, Russian and U.S. officials have refused to comment on any possible swap.
"A swap seems very much on the cards. There is political will on both sides, and actually by even moving it as far as they have, Moscow has de facto acknowledged that these guys were spies," intelligence analyst Pavel Felgenhauer said Thursday.
The arrests occurred more than a week ago, capping a decade-plus investigation of people who seemed to have embedded themselves in the fabric of American life. Authorities said they were reporting what they learned in the U.S. to Russian officials.
All 11 suspects were charged with conspiring to act as secret agents; nine were charged with conspiracy to commit money laundering. The indictment demanded that those accused of money laundering return any assets used in the offense.
The defendants were accused of living seemingly ordinary lives in America while they acted as unregistered agents for the Russian government, sending secret messages and carrying out orders they received from their Russian contacts.
The Associated Press contributed to this story.