The 20-year-old midfielder had enjoyed a three-month spell at Edgeley Park and The Hatters had hoped to complete a permanent deal for him.
Both clubs agreed a fee for the Republic of Ireland Under-21 international, but County decided to pull the plug on the deal after growing increasingly frustrated at Delaney's failure to decide over the move.
"Everything was agreed between ourselves and Stockport but Delaney obviously took too long to come to a decision," City boss Dave Bassett told the club's official website.
"As a result, Stockport have pulled out of the deal and I think it's now dead in the water."
Meanwhile, Bassett has admitted that a number of clubs are interested in signing Trevor Benjamin on loan until the end of the season.
The former Cambridge star has been out on loan at Crystal Palace and Norwich in the last two months and Bassett is willing to let him leave.
"We have had a number of enquiries from clubs wanting to take Trevor on loan for the rest of the season," said Bassett.
"I'm willing to let him go and the decision will rest with the player. He's not in my plans so we'll have to see what happens there."
