With city rivals Sheffield Wednesday entered administration this month, it emerged that COH had expressed interest in buying the club with the Owls' administrators.
It has been suggested that COH are exploring a merger between the two clubs. For now, COH have not denied the story.
BBC Radio Sheffield's Rob Staton wrote in a column today: "I've done a bit of digging and my understanding is there's truth to the original report of contact being made, although it's unclear precisely what the motivations were.
"It begs the question, what on earth were they thinking?
"What possible logical reason would there be to make contact? Did they think a merger was possible? Anyone in this city will tell you that if you think a merger is an option, you have absolutely no grasp of Sheffield football.
"Let's reflect on the last few months of COH's first year of ownership.
"They moved Wilder out of the club, appointed Ruben Selles and watched a promotion favourite drop into the Championship's bottom three.
"Red faced, they hastily brought Wilder back to rescue things and, now, this story.
"COH inherited a healthy club that has enjoyed plenty of success in recent years. They had/have a serial winner in charge of the football side of things in Wilder. There are highly competent people working behind the scenes.
"All they needed to do was offer support and leadership. They've done the opposite and created a situation where fans are rightly wondering if they 'get' their club or English football in general.
"If there was no enquiry and the reports and chatter are incorrect - say so. If not, and it's all true, it needs to be explained."