Cowley has revealed that he and his assistant, brother Nicky, have turned down Huddersfield's offer to manage them after compensation was agreed between the two clubs, believed to be £1million.
The West Yorkshire club are still looking for a new head coach since sacking German Jan Siewert on August 16.
It's been reported that the brothers were offered a £1.5million-a-year deal to move up a division, but feel the switch is not the right one for them to make at this time.
Speaking after Lincoln's EFL Trophy defeat to Doncaster, Cowley 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."
Its reported that the 40-year-old has also been in talks with another Sky Bet Championship side in Sheffield Wednesday, who still have caretaker manager Lee Bullen in charge, following Steve Bruce's surprise summer move to Newcastle.
The Cowley brothers joined the Imps in the summer of 2016, guiding 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.
The club have won the EFL Trophy and gained promotion to League One last season after winning Sky Bet League Two.
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