Reports in the national media on Tuesday afternoon claimed Cowley, one of the hottest young talents in the English game, was in advanced talks with the Owls over succeeding Steve Bruce at Hillsborough.
But hours later Cowley took charge of the Imps’ 3-1 defeat at Doncaster Rovers in the EFL Trophy.
Speaking at his weekly press conference, Cowley said: “There’s been no contact from Sheffield Wednesday.
“We’ve already spoken about Huddersfield (whom Cowley and his assistant manager brother, Nicky, turned down earlier this week).
“It would be nice to put it behind me (the speculation). You guys always seem to know more than I do.
“I can’t control what people say or what people write. All I can control is where my focus lies, which is fully on the game at Wycombe Wanderers on Saturday.”
Cowley took over at Lincoln in the summer of 2016, alongside his brother Nicky, leading them to National League champions, in the same season they became the first non-League club to reach the quarter-finals of the FA Cup for 103 years.
Lincoln also won the EFL Trophy before gaining promotion to League One last season after winning League Two. The Imps currently sit second in the table, two points behind leaders Ipswich Town.
Their outstanding track record and attractive style of play has won the Cowleys plenty of admirers.
Earlier this week, Danny Cowley admitted they rejected a big money move to Huddersfield Town, who welcome the Owls to the John Smith's Stadium after the international break. A £1m compensation package was agreed between the two clubs and the Cowleys were reportedly offered a £1.5million-a-year deal to move up a division, but they turned down the Terriers approach.
He said: "I think it has been widely reported that Huddersfield spoke with Lincoln. Compensation was agreed.
"For us, no disrespect to Huddersfield, who are an excellent club and have had an amazing period getting into the Premier League, but we have worked very hard at this football club over the years we have been here.
"I think we have built a real infrastructure from the academy and all the way through - we have a wonderful staff who we enjoy working with every day and we now have some fantastic facilities which we have worked really hard to build.
"Our club is in a really good place, so for us to consider moving our families and ourselves from this football club it would have to be the perfect opportunity."
The Imps boss said it would take a "perfect opportunity" to prise him away from Sincil Bank.
As for Wednesday, the Championship outfit are currently under the caretaker management of Lee Bullen. He was placed in charge of first-team affairs after Steve Bruce quit to join Newcastle United in mid-July.
The Owls have lost three of their last four league outings to fall to 11th in the standings.