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.
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.
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.