Gibson said: "We've played 13 games in the Premier League, not got the results we've wished for and already there's a noise about the continuation of the manager. It is nonsense.
"There has even been some trash about us having lined up a replacement. We know that's not true and Gareth knows that's not true. I've spoken to skipper Jonathan Woodgate and one or two others to tell them it's crap and to let the rest of the players know.
"We gave Gareth a five-year contract because he had to be given a chance to develop. He's a good man, with integrity and fantastic football experience. He will make mistakes as he's inexperienced but he has the intellect to learn from those mistakes.
"We know the manager's doing a very good job and in the club that's not questioned."