Rafa Benitez has been allowed to invest heavily in his squad since Hicks and Gillett arrived on Merseyside and is widely expected to steer Liverpool towards a genuine Premier League title challenge this season.
They currently sit fifth and are six points adrift of early pacesetters Arsenal, but Parry is adamant that despite suggestions to the contrary, there is no faction forming between the American pair.
"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," Parry told the club's official 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."