Gotze could have joined former boss Jurgen Klopp at Anfield in 2016 but opted against a transfer from Bayern Munich after the Reds failed to qualify for the Champions League.
The 26-year-old instead chose to rejoin Borussia Dortmund, where he was given his first-team debut by Klopp having come through the ranks.
Gotze has fallen down the pecking order at Dortmund this season, with his appearance in the midweek 1-0 Champions League win at Bruges only the second of the campaign.
And former Dortmund teammate Kevin Grosskreutz has told the player he needs a change of scenery, with Anfield the most attractive destination.