The Scotland captain is out of contract in the summer. Preliminary discussions between the two clubs have begun, with an outcome expected within the next few days, News.Az reports, citing Sky Sports.
Given the 31-year-old's contract situation and stated desire to resolve his future, Liverpool want to honour the huge respect they have for the player and his impact at the club since 2017.
Robertson joined Liverpool from Hull City and has been an instrumental part of their Premier League and Champions League winning teams.
But he has featured less frequently this season, making just four league starts following the addition of Milos Kerkez.
Robertson, who will captain Scotland at the World Cup in the summer, was wanted by Atletico Madrid in the summer but no move materialised.
