A report from the Daily Star claimed that Adams and former IMG and Chelsea executive Paul Smith had secured the backing of European investors for a £200 million takeover at Selhurst Park.
But Parish posted a link to the story on his Twitter account, along with a denial.
"This story is not true, there are no deals in place or discussions to sell the club," he said.
"I shook [Adams'] hand and [said] 'hello' once at an Arsenal game for 10 seconds, other than that I've never met him."
This story is not true, there are no deals in place or discussions to sell the club. https://t.co/aEvT20NTuQ— Steve Parish (@CEO4TAG) August 8, 2017
Responding to a reply from the journalist who wrote the Star story, Parish added: "No one has an option to buy the club, least of all Tony Adams and his mythical consortium."
Adams endured a forgettable spell as head coach of Granada at the end of last season, losing all seven games at the helm as the club were relegated from La Liga.