As far as I can tell, this rumor was invented out of whole cloth. One who gave voice to it was Democrat Congresswoman Jackie Speier, who claimed to have heard that Trump was not only going to fire Mueller, but was going to do it on a very specific day - Friday.
The more that's come out the past few days about rottenness at the FBI and within the Mueller investigative team, the more we start hearing media speculation that Trump is getting ready to fire Mueller. That would seem to be monumentally counterproductive, since it looks more and more like there's not going to be anything tying Trump to "collusion with Russia," and the best possible outcome would be for Mueller to finish his investigation and admit that. Does Mueller deserve to be fired? I'd say yes. But it benefits Trump more to let him wrap this up.