Anfield side track experienced Uruguayan.
Liverpool are hot on the heels of experienced Benfica defender Maxi Pereira according to the Daily Mirror.
The 30 year old Uruguayan international is seen as a cost-effective replacement for soon to be out of contract right-back Glen Johnson and could be available for as little as £4m as his Primeira Liga employers seek to cash in on the tigerish battler.
Brendan Rodgers has also taken a keen interest in Barcelona’s Martin Montoya though efforts to land the 23 year old Spaniard have been ongoing for quite some time.
A move for Pereira may prove more likely in January though Besiktas and Trabzonspur are also interested.
Rodgers could look to elicit the services of former star Luis Suarez to help persuade Pereira to consider a move to Merseyside.
Pereira moved to the Portuguese capital back in 2007 and may be ready for a fresh challenge.