Leppitsch signed a one-year contract extension in March but has come under immense pressure this season, with the Lions winning a total of three games to sit 17th on the ladder.
The report claims Leppitsch is “coming to the realisation that he will not see out his contract”.
Matthews, who coached Brisbane to three consecutive premierships in 2001-03, returned to the club in 2013 as football director on its board.
The deputy chairman is set to resign according to Fairfax, with the report claiming the legend is “disenchanted at the perceived lack of assistance from the AFL”.
Brisbane are dealing with many serious challenges, both on and off the field.
That long list includes $13 million debt, dwindling crowds and a so-far fruitless search for a new base because of substandard facilities at the Gabba.
Many pundits have been critical of the AFL for not offering some form of list concession, such as the re-introduction of a retention allowance given how much talent has left the club.
Leppitsch opened up about the issue after a 138-point loss to Adelaide earlier this month.
“We’ve been given nothing as a footy club,” he said at the time.
“No extra concessions and money. GWS bought Heath Shaw and (Shane) Mumford with the extra footy concessions they got.
“You’ve got to understand there’s a system behind what you see out there on game day.”
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