The actor's alleged affair with Ryan was said to have caused his split from partner Susan Sarandon last December after 23 years together.
However, Robbins insisted that the two were never in a romantic relationship and denied that they went on a date just weeks ago.
"Apparently I'm dating Meg Ryan right now. That's pretty weird. Apparently I saw her a couple of weeks ago. When I was in New Orleans and she was in LA," he told Uncut.
"That time travel thing, it's pretty impressive that I can do that. I'm always hearing odd stories about myself, and snide remarks from critics. I try not to take too much notice."
A rep for Ryan also dismissed the reports, saying that the pair are simply "great friends".