The 24-year-old midfielder has established himself as a regular starter in the Portuguese club's first-team following the summer departure of Javi Garia to Manchester City.
Now, Reds boss Brendan Rodgers wants to bring the Serbian international to Anfield in January, as he looks to bolster his ranks in the middle of the park on Merseyside.
However, Liverpool's hopes of securing a deal for Matic have been dealt a significant blow after O Jogo reported that Benfica are on the verge of extending the player's contract until 2018, also increasing his minimum fee release clause to €30million.
If that agreement does go through, it will almost certainly end the Premier League club's pursuit of Matic, with American owners Fenway Sports Group keen not to make the same mistake as when they ploughed almost £70million on players like Andy Carroll, Stewart Downing and Jordan Henderson, who have all failed to live up to expectations.
Instead, the club will operate a more reserved approach in the transfer market, as Rodgers continues his search for value-for-money reinforcements in the New Year.