Nobody will believe that rumor.
The rumor was without foundation.
その噂は本当であるはずがない。
That's because I don't suppose anybody will believe this story.
That rumor is definitely a lie.
I do not care about gossip.
That kind of rumor is groundless.
I don't know the origin of the rumor.
To the best of my knowledge, the rumor is not true.
To the best of my knowledge, the rumor isn't true.
He isn't the kind of stupid person who would believe that rumor.
That rumor has come to be believed as the truth.
Almost all the people believed the rumor.
I know of him, but I don't know him personally.