With Carragher set to retire following Sunday's final game of the season against QPR, Reds boss Brendan Rodgers is on the look-out for an experienced man to come in and replace him.
Reports in Spain suggest that Real defender Albiol has decided he wants to leave, having fallen out of favour with Jose Mourinho, and that has apparently alerted the Reds.
The 27-year-old is keen to ensure he stays in contention for a World Cup place for Spain in next summer's World Cup in Brazil and would be open to a move to Anfield.
Rodgers is currently looking for alternatives to Carragher and had identified Ashley Williams at his old club Swansea but Arsenal are also keen on him and that potential deal has stalled in recent weeks.
Albiol could be the experienced centre-half the Northern Irishman is looking for and he could be available for around £6-8million, although with Mourinho expected to leave Real this summer and return to Chelsea, it is by no means a certainty he will still want out when the transfer window reopens.
Liverpool last week