A rumor was a statement, true or untrue, that was gossiped or speculated about.
According to T'Pol, as of 2152, the Romulans were rumored to be an "aggressive, territorial species". (ENT: "Minefield")
In 2267, when James T. Kirk professed his innocence in Benjamin Finney's untimely death to Areel Shaw, she told him that wasn't what rumors indicated. (TOS: "Court Martial")
In 2364, William T. Riker noted that everything the Federation knew about the Romulans up to that point had been based on rumor or conjecture, (TNG: "The Neutral Zone")
As of 2368, Riker had heard rumors about The Children of Tama for years. (TNG: "Darmok")
In 2370, Kalita informed Ro Laren of a disturbing rumor she'd heard from a trader on Pendi II; namely, that the Cardassians were going to supply colonists with biogenic weapons. (TNG: "Preemptive Strike")
As of 2375, Son'a starships were rumored to have isolytic weapons. (Star Trek: Insurrection)