Leeds City Council has withdrawn a £4million grant which has placed the redevelopment of the stand Yorkshire shares with rugby teams Leeds Rhinos and Yorkshire Carnegie under threat.
While Denison says the Ashes Test Headingley will host in 2019 does not depend on the rebuilding of the stand, needed to satisfy modern requirements, the four World Cup matches the ground is due to stage in the same year does.
And unless Yorkshire can raise the reported £17million they need for the upgrade, they will not be able to apply to host any Test matches at Headingley from 2020 - when its staging agreement with the England and Wales Cricket Board ends.
The development would also impact their hopes of being one of the hosts for the new domestic Twenty20 competition, set for its inaugural staging in 2020, and with construction needing to be started by the end of the season, Denison et al are searching for an urgent resolution.
"Discussions are ongoing all the time formally and informally [with the council] to try and find a solution because it is bonkers if the city, county and the club are running the risk of losing international status," Denison told the Daily Telegraph.
"There is no guarantee we would be able to host one of the new T20 teams as we haven't got a stadium up to scratch. It does look quite gloomy but nobody is giving up. We are going to keep going but it is hard work.
"The Ashes Test at Headingley will happen at 2019 anyway as it is not predicated on anything. But the World Cup games are predicated on us finishing that stand, so if we want to get it done by then we have to be cracking on by the end of this cricket season.
"That is only a matter of weeks away in construction terms plus there will be a substantial amount of preparatory work that has to be done before bulldozers move in and knock down the existing stand. It is why everybody is working really hard to find a solution."
Durham's financial plight led to their Chester-le-Street ground losing Test status as part of a string of penalties.
And it may be with that in mind that Denison is unwilling to take a risk in order to satisfy the requirements needed to bring Headingley up to scratch.
He added: "The last thing we want to do is mortgage the future at all costs. Having a club that can sustain itself is the most important thing. We are not going to risk that because of the situation we find ourselves in right now.
"We don't want to say, 'Don't worry, let's just borrow up to £40m and pay it off over 40 years.' It is an unimaginably long period and who knows what will happen in the next four years let alone 40."
