Kennedy was one of several coaches who have held discussions with the Scottish Rugby Union in recent months, following the departure of New Zealander Todd Blackadder.
But Edinburgh Rugby Limited chief executive Alex Carruthers confirmed Kennedy is not, contrary to speculation, about to become the next head coach of the team.
He said: "We are discussing the head coach position carefully with a number of key people, including our partners in Scottish Rugby and we are also conscious that many of the players are already back in training this week.
"So ideally a head coach appointment should be made soon but it's important to get this right.
"We are making steady progress on a suitable appointment. I'm confident the right decision will be made in due course."
SRU chief executive Gordon McKie added: "The appointment of the head coach for the Edinburgh Gunners is now in the safe hands of Edinburgh Rugby Limited.
"We are advising and working well with Alex and his colleagues, and are confident they will make good decisions in the best interests of the Gunners."