Graves fears they could go to the wall unless there is a radical overhaul of the English game.
Graves was among those who pressed for a far-reaching review currently taking place into county cricket.
The Morgan Report – spearheaded by former International Cricket Council president David Morgan – is an England and Wales Cricket Board initiative designed to produce a blueprint for a vibrant domestic game.
The report, which is seeking the views of the 18 first-class counties, is due to be published later this year.
Although Graves admitted Yorkshire had yet to determine their own proposals, he is adamant English cricket needs some kind of shake-up if one or more counties are not to go under.
“I think there is a serious risk of some counties going bust,” said Graves. “When you look at it, some of the counties, the returns they make on what they’ve got and the profits they generate, will never justify being a business really.
“The problem we’ve got with the county game is that the majority of counties are struggling for cash.
“Unless we address that, there is definitely a risk of clubs going under.”
Sixteen of the 18 first-class counties recorded losses last year, which amounted to more than £9m.
Yorkshire had a pre-tax deficit of £2m following their decision to stage the Pakistan-Australia Test, while Warwickshire (£2.8m) and Lancashire (£2.1m) also took heavy hits.
At the lower end of the spectrum, Leicestershire’s deficit of £405,000 threatened their very existence.
Graves said he had no magic solution but stressed there were obvious areas that could be addressed. “I haven’t got a blueprint as such, but we definitely need certainty going forward in terms of the formats of cricket that are being played and when the matches are played,” he added.
“At the moment, the players are complaining there’s too much cricket, the members are saying the fixtures are all over the place and we need a better appointment-to-view so that people know when games are taking place to help increase attendances and bring in more money.
“I’m the chairman of Yorkshire County Cricket Club but if someone says to me, ‘Where are Yorkshire playing?’ I haven’t got a bloody clue.
“I’ve got to get a bloody fixture list out because I don’t know when we’re playing from one week to the next – and neither does Joe Public. The fixtures are all over the place.”
Although Yorkshire are £20m in debt, they have structured repayments in place to clear those debts by 2019 and are effectively bankrolled by Graves, the multi-millionaire chairman of the Costcutter supermarket chain.
Some of their county brethren are not so fortunate, but Graves is adamant any solution going forward must retain the 18-county structure.
“Rather than cull the number of counties, I think there needs to be a restructuring of the game that makes it viable for everyone to survive,” he said. “But if things stay as they are, there are bound to be problems because the situation cannot continue as it is.”
Graves said one solution – although not necessarily his personal choice – would be to revamp the County Championship.
Instead of two divisions of nine teams playing 16 games, he said there could be three divisions of six teams playing fewer matches.
“I’m not saying I want that to happen, but the key point is that I’m open to change and I think English cricket in general needs to be open-minded,” he added.
“At the end of the day, there’s all sorts of things you could do.
“You could have three divisions of six and fewer games; you could even change the financial handouts that are given to the counties by the ECB.
“Instead of having a flat £1.8m annual handout to everyone, regardless of which division you’re in, you could give the First Division clubs £2.5m, the Second Division £1m and the Third Division £0.5m, or whatever.
“By doing that, it would be a bit like football in that you reward the top division and penalise the third division.”
Graves believes cutting the counties is the soft option. “It’s always easy to say get rid of two counties, get rid of four counties, so there’s more money for everyone else, but I think that’s a bit mean,” he added.
“We can’t say, for example, just because we’re Yorkshire, that we should get rid of two or four counties. What right have we to say that?
“If you look at Leicestershire, they are one of the least financially viable counties of all in terms of attendance and membership figures and yet they went and won the Twenty20 Cup this summer, whereas we haven’t even reached a Twenty20 finals day.”
Inside, the first of our three-part series looking into the state of the game: Page 22.
Cricket’s new Test: Page 12.