The former England international joined Liverpool from Manchester City on a free transfer in the summer of 2015.
The length of his contract was not revealed at the time but according to The Sun, the terms of his deal means he can stay until 2020.
Milner has been utilised as a left-back under Jurgen Klopp since the German's arrival and his performances have impressed him.
James Milner is in line to stay at Liverpool until 2020
Liverpool player ratings against Manchester City
Sun, March 19, 2017
Click through the gallery for the Liverpool player ratings against Manchester City
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Click through the gallery for the Liverpool player ratings against Man City
Jurgen Klopp has been impressed with James Milner this season
The report claims Klopp is happy for the 31-year-old to remain at Anfield and continue to be part of his plans going forward.
There is understood to be no planned talks over extending his deal with Milner and Klopp both satisfied with his current terms.
Milner has been a key part of Liverpool's success this season at left-back with Alberto Moreno struggling to displace the former Leeds star.
Most valuable Premier League XI in a 4-2-3-1 formation
Mon, March 20, 2017
Express Sport brings you the most valuable Premier League XI in a 4-2-3-1. Players' values according to Transfermarkt
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GK: Thibaut Courtois (Chelsea) – £34.00m
James Milner scored in Liverpool's 1-1 draw with Manchester City
Klopp's first-choice left-back was on hand to secure Liverpool a point on Sunday as Milner converted from the penalty spot in their 1-1 draw with Manchester City.
Liverpool sit fourth in the league table, 13 points behind leaders Chelsea.