Co-owners Tom Hicks and George Gillett held talks with Klinsmann, claiming soon afterwards they did so because they were unsure of Benitez's "commitment to the club".
Benitez, however, seems unlikely to be appeased by that account of events, given his existing rift with Parry.
"Off the pitch, I am surprised at things I have read," he said. "I need some clarification about a meeting with a lot of people that I did not know about.
"I will talk with the board about this (the Klinsmann issue) - as soon as possible, today or tomorrow. I need to resolve questions and I want some answers. I want to clarify things. I am really calm - but I want answers."
It is the allegation of Parry's involvement in the Klinsmann talks that most concerns Benitez.
"I need to talk to the board to clarify things," he stressed.
"I was surprised about a meeting with another manager. What concerned me was the people who were in the meeting."