The 54-year-old died yesterday following a fall on Sunday morning.
Former team mates at Aberdeen, and both part of the side which won the European Cup Winners Cup in Gothenburg in 1983, McLeish said he last saw Cooper last saw Cooper at a reunion event just over a fortnight ago in Aberdeen.
“It’s horrible, tragic,” he said.
“Neale had a heart attack last year and I didn’t know many details this time other than he had a fall at home,” McLeish said.
“I’ll be in touch with Neale’s family. It’s horrific to hear this bad news.
“Neale was a massive character, a tremendous lad and always was throughout his career,” added McLeish.
“He was such an affable guy. I was praying he would pull through.
“He was a battler and we were all together in hoping he would pull through.”
“I saw him last at our Gothenburg night a few weeks ago and he was in such good spirits,” he added.
“I spoke to him about his heart attack and he said he was recovering well. I knew that anyway because his family had kept me up to speed.”
A statement from Peterhead also paid tribute saying: “Peterhead FC wish to express their sincere sadness at the passing of former manager Neale Cooper.
“Neale was an infectious character who was well loved by everyone at the club during his tenure as a coach and manager.
“Our condolences are extended to Neale’s family and wide circle of friends at this difficult time”
McLeish recalled his first impressions of Cooper when the pair first met.
“I saw him when he was 14 and I arrived on the training ground and he stuck out a mile,” he said.
“I remember thinking: ‘Who’s that guy – he’s absolutely brilliant’. Then, because of the partnership Willie [Miller] and I formed he moved in to midfield and he became a very good footballer with a very aggressive style of play, but then he could do everything.
“I’ll never forget seeing that curly mop of white curls walking into the training ground. I thought we had a top, top player in our midst and I wasn’t wrong. I was 17, he was only 14, but he wasn’t overawed.”