Gotze, 29, has been out of contract since leaving Borussia Dortmund at the end of the 2019/20 season and has now been tipped to return for a second stint at the Bundesliga champions.
In what would mark as a surprise move for the technically gifted playmaker, the loan returns of Phillipe Coutinho, Ivan Perisic and Alvaro Odrizola has left Flick looking towards adding some depth to their current squad.
According to Sport Bild, Gotze has been contacted over returning to the club where he departed in 2016 after failing to command a regular place in the starting XI under Pep Guardiola after first leaving his boyhood club.
It's believed that Flick had requested the club's board to sign Kai Harvertz and Timo Werner who both opted for moves to Chelsea and he's now informed club bosses Karl-Heinz Rummenigge and Brazzo Salihamidzic that Gotze is a priority.
The 63-time capped Germany international scored 22 goals and added a further 21 assists in 73 league games during his time with the Bavarian giants.