
The two US businessmen completed their takeover of the club earlier this year, and provided substantial backing for manager Rafa Benitez in the summer transfer market.
They have also overseen the development of plans for a new stadium.
Newspaper reports Sunday suggested that the two had fallen out but Parry insists they are still working together closely.
"I've just spent a couple of days with Tom and George and both of them were in good spirits working hard together on future plans for the club," he told the club website.
"I wouldn't normally comment on these things but a story in one of the Sunday papers claiming there was some sort of problem between the two couldn't be wider of the mark. In fact, it's absolute nonsense."