A spokesperson for Hillary ClintonHillary Rodham ClintonSecret CIA assesment: Russia was attempting to assist Trump Joy Behar: Why do I have to be nice about Trump? Poll: Republicans think media ‘intentionally misled the public’ about polling MORE says she is "perfectly willing" to debate Democratic presidential rival Bernie SandersBernie SandersDemocrats: Where the hell are You? Sanders on Trump pick: This is how a rigged economy works Trump picks Goldman Sachs chief for top economic adviser: report MORE in New York.
"If they can find a mutually agreeable date in the next couple of weeks before New York, I think it could happen," Fallon added.
During a campaign stop in LaCrosse, Wis., on Tuesday, Clinton told reporters she was open to the idea of debating but didn't suggest a date, according to the New York Daily News.
Sanders seized on the apparent openness, saying later on CNN, "Let's do it."
The campaigns have been sparring for days over whether to hold a debate in the coming weeks, with the Sanders campaign issuing a letter over the weekend suggesting Clinton is afraid to debate.
Clinton released a new campaign ad Wednesday aimed squarely at Republican rival Donald TrumpDonald TrumpMichigan Supreme Court shuts down Stein's recount effort Secret CIA assesment: Russia was attempting to assist Trump Trump closes four companies tied to Saudi Arabia MORE in New York ahead of the state's primary.
--This report was updated at 11:32 a.m.