Neilson guided Hearts to Scottish Championship success at the first time of asking this season, with seven games to spare.
Former fans favourite at Hearts, Pressley, was relieved of his duties at Coventry in February after a disappointing season in League One.
But he has been impressed with Neilson and his development and even tried to bring him to Coventry.
“I wanted to take him to Coventry. He came down and spent some time with us. If I could have got the right financial package, you might not be talking about him being the Hearts manager right now,” he told the Edinburgh Evening News.
“I would’ve had him in at Coventry. Unfortunately we couldn’t do that and his path has led to Hearts, where he’s done a terrific job.
“There has to be a real appetite to learn and the enthusiasm he has is important. He also has certain ideas on the game and a great way with people. Those components were going to be key to him becoming a good coach and manager.”