The pair were reported to have fallen out over the summer due to the club's transfer policy, but Parish has branded the rumours as "ridiculous".
"I can't give it a moment's credibility," he told the London Evening Standard. "It's ridiculous, there is just no grounds to any of it.
"Ian is our manager. We are very happy for Ian to be our manager. We all have a great working relationship and we're focused on one thing, the retention of our status in the league.
"I regularly go down to the training ground; there is no problem at all. Ian wants to stay here and build something. Right now we couldn't be more together as a group of people and couldn't be more focused on the goals that we've got."
Holloway took charge of the Eagles in November of last year.