The current GAA TV rights deal means there is a possibility that a couple of high-profile provincial matches won't be shown live this summer.
The Monaghan-Tyrone match is a likely casualty this season and Quirke believes there should be a facility for fans to view all the matches played each weekend.
"I don't like it - the Ulster Championship has always provided us with the best entertainment from these earlier round games. I know everything is being pushed to the Super 8s and those games are obviously going to be really competitive but then everyone is going to want to show all those games.
"But, somebody should have seen this coming down the track that we could have some system in place to be able to watch these games in Ulster or to a lesser extent, maybe the games in Munster.
"I still can't understand how we don't have a facility - whatever way they want to work it out, there's plenty of intelligent people in Croke Park that could work out these deals - how we don't have a facility where I can watch games in whatever county I want to watch them in - whether the county have to put them on themselves or stream them or deferred coverage or something but how we can't, in this day and age, that I can't go and watch an Ulster Championship game on my laptop or on TV or on deferred coverage - it makes no sense.
"And, surely we have the facility, even if it's one camera at a game - surely, surely, there's some mechanism there."
Asked about the possibility of paying for such a service, Quirke said: Personally, yeah I would. I'd pay money for it if I had to. I know people will start giving out if we have to start paying for our national games but if it's a facility whereby I can go and watch more games on my laptop or stream it on my TV - personally I would be willing to pay for it," he added.
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