Former triple premiership-winning Lions coach Matthews is believed to have joined forces with Brisbane directors Paul Williams and Mick Power and are running a ticket to challenge the board.
Johnson reportedly refused to stand down when challenged by Williams and Power at a Lions board meeting on Wednesday morning.
Johnson's fate now looks set to be decided by an emergency general meeting.
It is understood Matthews, Williams and Power have the support of Lions powerbrokers who have lost faith in Johnson due to Voss' recent sacking and want to launch a fresh push for Sydney's premiership-winning coach Paul Roos.
A successful coup could result in Matthews being ushered into a football director's role at the Lions.
Williams hoped the split in the board would be resolved quickly but claimed his faction was up for a fight.
"We would hope there is sufficient momentum from our actions for the remaining board to reconsider their position," he told The Courier-Mail website.
"We hope for the good of the club they might decide there is no point going to a meeting, but we are prepared.
"Leigh has taken a long, long time to get to this point, he feels now is the time to make a contribution.
"He has made it clear to us that he wants to be part of our ticket."
Matthews said he had knocked back several approaches to return to the Lions since sensationally ending his coaching stint in 2008.
However, he changed his tune and decided to join a ticket when convinced the club's best future was under a Power-Williams led board.
"My jump over the cliff was when Paul and Mick said they were going to run for the chairmanship and deputy chairmanship," he told The Courier-Mail website.
"I know these people well and believe in what they are doing.
"I'm on because of them and I believe I can help."