Carragher, 36, retired from playing football last year after an illustrious career with Liverpool, his boyhood club.
Now a pundit for Sky Sports, he has admitted he hasn't closed the door on a return to the club, if the role was right.
''If I was offered a job at Liverpool in a good coaching role, it would be difficult to turn down,'' Carragher is quoted by The Star.
'I suppose because it's your club, you always want them to do well, but like I said, I am happy now, I enjoy what I am doing but i that happens you have a decision to make.
''Anyone else but Liverpool you wouldn't really change your job but when it's your own club it's a big pull.''
Many fans have cried out for Carragher to return to Anfield in a coaching capacity ever since he announced his exit and retirement.
The 36-year-old made over 700 appearances for Liverpool in all competitions and won 38 England caps, with the majority coming between 2004-2006.
A knowledgeable and experienced defender, Jamie Carragher can now be seen on several Sky Sports panel shows, most notably Monday Night Football [MNF] with former England teammate Gary Neville.
Both Neville and Carragher have been praised by football fans for revolutionising punditry on television, as their knowledge generates more interest in the science of the game.
Sky, perhaps, won't be too happy with their employee's comments about wanting an Anfield return, but Liverpool fans will no doubt be left excited at the prospect of hearing his feelings regarding a comeback.