Parry said, "It was fairly public at the time so it's not really a revelation. I think it was pretty serious. For Rafa it was obviously a temptation because Real Madrid is his club; he's been there as a player and a coach, so it will always be an opportunity he'd have to consider."
Parry added that he had talked with the Reds' boss about the offer, but the city and the club's success and future plans had persuaded him to stay on at Anfield.
"We sat down for a few hours together and talked about the direction the club was going in," Parry said. "He enjoys being in Liverpool and his family enjoys being in Liverpool, and the point is, he believes in the direction we're taking and that our mutual ambitions match."