However, the ex-Republic of Ireland international could've joined Blackburn Rovers instead of Man Utd back in the early nineties in a record-breaking deal.
He added: "They [Man Utd] offered me three-hundred thousand a year,
"It was important, because this is the business side of the football, and straight away I learned about Man United was that it is business, as well.
"I'm thinking, it's not a massive rise, especially considering it's going to be a transfer record. So, they stalled a little bit, and dragged their heels."
As a result, Keane accepted Man Utd's £350k-a-week offer and joined them from Nottingham Forest in a £3.75m deal.
However, a jilted Dalglish wasn't done there, and as Keane tells it, threatened 'to find' the midfielder.
"He was effing and blinding (on the phone), saying 'you're a f**king disgrace," Keane said.
"I said, 'listen, I'm going on me holidays next week', which I was, I was going to Cyprus with a few lads... just to do some sight seeing.
"'I'm going to Cyprus with me mates, and when I come back I'm going to sign for Man United'.
"He said: 'I'm going to find you. I'm going to come to Ayia Napa and find you. So, every bar in Ayia Napa, I was looking over my shoulder waiting for Kenny Dalglish to walk in."