"We have reason to believe that one of those Americans will be released today," Sullivan told NBC's "Meet the Press."
Sullivan declined to give the identity of the hostage who might be released. When asked whether it was a 4-year-old girl whose parents were killed, he said: "We have a sense of who it is but I am just not in a position to confirm it."
U.S. television network Fox News reported that 4-year-old U.S. citizen Abigail Edan was expected to be released on Sunday. Fox News said an "official source" confirmed that Edan was expected to be released, but did not name the source.
President Joe Biden and Israeli Prime Minister Benjamin Netanyahu have a call scheduled for later on Sunday, Sullivan told CBS News.
Israel and Hamas have agreed to swap 50 hostages held by the Palestinian militant group for 150 prisoners in Israeli jails over a four-day truce period.
So far, Hamas has released 26 Israelis and four Thai nationals it had held as hostages, while Israel has freed 78 Palestinians.
Egypt, which is helping to mediate the deal, says it has received lists of 13 Israelis and 39 Palestinians scheduled for a third release on Sunday.
It is the first halt in the conflict since Hamas fighters rampaged through southern Israel on Oct. 7, killing 1,200 people and taking about 240 hostages.
In response to that attack, Israel vowed to destroy the Hamas militants who run Gaza, bombarding the enclave and mounting a ground offensive in the north. Palestinian health authorities say some 14,800 people, roughly 40% of them children, have died.
(Reporting by Andy Sullivan and Moira Warburton in Washington and Jason Lange in Buffalo, NY; Editing by David Goodman, Alexander Smith and Mark Porter)