Carragher will play his final game for the Reds against Fulham on Sunday afternoon as the curtain comes down on an Anfield career that has spanned 16 years.
The defender has always been fully committed to the club and even though he always planned to see out his career with Liverpool, he is still surprised that no offers came in to try and take him away.
"I never really had the option to leave - I don't know whether it was a good thing or bad thing," Carragher told The Sun. "Maybe no-one rates me!
"I've never even been close. My agent has never rang me up and said, 'This team fancy buying you'. Not once.
"Maybe I was always seen as 'Mr Liverpool', I suppose. You'll have to ask different managers. But I'd never have left in any circumstances. Maybe those managers realised that. Or, like I said, they just didn't fancy me.
"And I can't say I ever thought about leaving when I wasn't in the side. You have good times and bad times at your club. It's like being a supporter. You don't stop supporting your team because of a bad run.
"And we've had some great times here, won some big trophies. So I feel lucky and privileged."