The Parkhead club have had at times an uneasy relationship with the vociferous and political section of the Hoops support, who boycotted Saturday's 6-2 Clydesdale Bank Premier League win over Dundee United at Parkhead, due to what they claimed to be "the continued police harassment of our members".
The fans' group released a lengthy statement airing their grievances which they say has led to a situation where "any relationship with the club has completely disintegrated".
Within the statement was criticism of Celtic chief executive Peter Lawwell and Hoops boss Lennon for allegedly not addressing their concerns.
The Parkhead club responded with a statement which promised that "each incident or complaint will be investigated" while also saying: "Accusations suggesting that the Club is in some way involved in targeting supporters are ludicrous.
"These accusations have absolutely no foundation whatsoever and, of course, are very disappointing."
Ahead of tomorrow night's visit to St Johnstone in the SPL, Lennon, who has often backed the Green Brigade for the noise and colour they bring to home games especially, was looking for resolution.
He said: "I have had no direct contact (with Green Brigade). We did make an offer to speak to them a while back but they never came forward.
"There is no need for all this unnecessary conflict between any group of supporters and the club because we are moving well on and off the field.
"The club have always maintained an open stance on it, that if anyone has a legitimate complaint the club will look at it and deal with it as best they can and that has never changed.
"They (Green Brigade) are an important part of the club, they have brought an energy and a freshness to the stadium and I have been quite supportive of that.
"However, there is no collusion between the club or any of the authorities to dampen that.
"Our main concern is health and safety within the ground and, as I said, if anyone has a grievance, write to the club, who have helped in the past as best they can and have helped in a lot of ways and that stance remains open to the Green Brigade."
Strathclyde Police are aware of the Green Brigade's complaints but have yet to respond.