Cooper, 46, had been linked with a move to Hillsborough to work alongside Wednesday’s new head coach Carlos Carvalhal, but Power claims the local media “created stories”.
Power told BBC Wiltshire: “You have to appreciate I don’t live in this country, but it’s quite frustrating when I read certain things.
“Certain media outlets that need to sell papers and do certain things in summer, that’s their business, they try and create stories and say certain things and want people to respond.
“I never had an official approach from Sheffield Wednesday, I never heard from them at all.
“When no one makes an approach and newspapers come up with these stories, I don’t make any money and nor does the football club out of selling papers and that’s why there’s no reason for us to respond really.
“If there was an approach and Mark was going to go and speak to them then I’d let the fans know, of course I would. When nothing’s happened I don’t see the point in it really.”
It had been reported that Cooper was sounded out by Wednesday but he was not keen on leaving Swindon to become an assistant.
Wednesday were understood to be keen on a British coach to work alongside Portuguese Carvalhal and considered offering Cooper the role of head coach under a director of football.
But following delays which served to fuel the speculation, Carvalhal was installed as Wednesday’s new head coach at the end of last month.
Cooper told the local media after his side’s friendly defeat to Swindon Supermarine on Tuesday night that it was business as usual at the County Ground.
“I think when jobs come up there’s a lot of speculation isn’t there,” Cooper said.
“If you’ve had a reasonable season as a manager you get linked to jobs.
“Speculation was rife and I got linked to (the Wednesday job), I’m not sure if there was an approach or not, but it’s probably best leave that one to the chairman.
“I’ve got a job to do and I’ve got another season to go and I’m really looking forward to it.”