The Wales No.8 has a year left on his contract at Rodney Parade but has been increasingly linked with a move away from the region.
Bath are among a host of clubs reportedly interested in acquiring Faletau's services but the Dragons are adamant he will see out his current deal.
And their forwards coach Rob Appleyard has praised Faletau's professionalism and commitment during the speculation.
"I don't think it's fazing him," said Applyard.
"Toby turns up and trains as hard as anybody, whether he's just come back from an international campaign or whether he's been with us for a few weeks.
"He's a one-off character without a shadow of a doubt. He's a really good rugby player.
"We can talk about a new line-up set-up, which he's never heard of before and he goes in and delivers it having heard it just once.
"So he's a very coachable player and listens a lot. But one thing that's on my mind is we wouldn't want to overcoach him so he loses his X-factor.
"It's almost the way he runs he doesn't care. He runs as though he doesn't even know people are trying to tackle him sometimes. He just seems to run and beat people."
Faletau burst onto the international scene in 2011 and has established himself as one of the most dynamic back-rowers in the game.
He has been linked with a place on June's Lions tour to Australia and Appleyard reiterated the Dragons' desire to hang on to their prized asset.
"We want Toby to stay. We understand it's not always that easy," added the former Wales flanker.
"If you are being offered double or treble your wages, would you take it to move to the south of France? I am sure most people would contemplate it.
"Obviously we want to keep Toby with us. He has got another season with us. It's out of my remit, but I'm sure talks are going on behind the scenes to retain Toby's services.
"But, at the end of the day, it comes down to what the individual wants to do."