The Reds are repeatedly linked with the talented midfielder, but do not need the Spaniard currently.
The Real Madrid deep-lying playmaker has fallen down the pecking order at the Santiago Bernabeu and is widely expected to be a fringe figure if he stays in the Spanish capital.
Liverpool fans remember Xabi Alonso fondly from his time at Anfield, with Illarramendi being compared to the former Reds star over the years.
However, Brendan Rodgers’ men would be foolish if they were to move for the former Real Sociedad midfielder.
The Northern Irish manager has clearly opted for Jordan Henderson and James Milner as his first-choice central midfield partnership - which has meant that the supremely gifted Emre Can has had to start both of the side’s games on the bench.
With Lucas Leiva and Joe Allen also in the Reds first-team squad and only two central midfield positions in Rodgers’ 4-2-3-1 formation, adding another player in this role seems unnecessary.
Can was one of the club’s better performers last season and has shown that he has an excellent range of passing and positional sense when he plays in the boiler room.
If the German under-21 star can’t get into the current Liverpool team, signing Illarramendi - a player with similar attributes - would not be the smartest move.
There is no doubt that the Spanish star has all the assets to be a success in the Premier League, but for the time being it doesn’t make any sense for Liverpool to move for him.