Maynard has been linked with a £4 million move to the Cottagers.
"This is nothing more than press speculation and, just because something is reported in a newspaper, does not mean it is going to happen," Lansdown told the Bristol Evening Post.
"If Fulham or any other club wants to talk to us about one of our players, then they should contact us directly rather than go through the media.
"At this moment in time, there has been no interest shown by any club in any of our players."
He added: "We know Nicky well and we know his agent and have a good relationship with him. He wouldn't be putting these stories about."