But instead the Liverpool board moved for former Fulham manager Roy Hodgson to take charge.
Dalglish commented on the Liverpool job in his new book ‘Dalglish in his own words’.
He wrote: “It was right for everybody that Rafa Benitez left – for him and for Liverpool Football Club.
“There just comes a stage in every manager’s career when the board says, ‘You’ve been good for the club but we feel it would be best if you go’.
“Sometimes it works the same way for a manager – ‘I’ve done my time. There’s no animosity but it’s time to have a go somewhere else’.
“When it was clear Rafa was going, Christian Purslow asked me to get involved in the selection process for the next manager.
“I had to let them (the board) know my real views. I wanted the job. I couldn’t miss the opportunity.
“One day, I was in a meeting with Christian and the chairman, Martin Broughton, and I formally put my name forward.
“‘We don’t want you, Kenny’, came the reply from Christian and the chairman. Fine. That’s their prerogative. They explained they had different plans for me, a position with greater longevity.”