The 22-year old striker is being heavily linked with a move away from Tannadice this summer with Scottish champions Rangers showing considerable interest.
Recent reports suggested that the SPL Young Player of the Year was set to hand in an exit request but Houston has quashed those rumours.
"I've heard these rumours about David and they are absolute nonsense," he told the Daily Record.
"I sat with David and the rest of the boys in our hotel. David's banter was great, as it always is. Everything that's going on is not affecting him one bit, he's not that type of boy.
"For anyone to suggest he will put a transfer request in is ridiculous.
"I have spoken to David one-to-one, he trusts me and knows I am telling him everything.
"One thing that has not happened in our discussions is him saying he wants a transfer. It's total rubbish."