Gotze is set to become a free agent after Borussia Dortmund confirmed last week that the two parties will be parting company for a second time at the end of the 2019/2020 season.
Gotze is in his second spell as a Dortmund player, having initially departed for a three-year spell at Bayern Munich in 2013 before returning to the Signal Iduna Park in 2016 on a four-year contract.
The 27-year-old has been a shadow of his former self since his return as he has battled injuries and struggled to hold down a regular place in the Dortmund first team.
It represents a major fall from grace to grass for a player who was tipped to take the world by storm after scoring the winning goal for Germany at the 2014 FIFA World Cup final but Ter Stegen is hopeful Gotze can get his career back on track in Spain.
The Blaugrana number one told the Kicker meets DAZN podcast: "Mario is a player who can handle the ball and advance the game. He would definitely fit in the Spanish league.
"Whether his goal is to play football - I don't know. When we talk to each other, we never talk about football.
"For me, it is only important that he makes the right decision and that he is happy. It would suit a lot of clubs and can make a difference for many clubs."
Gotze has made 15 appearances for second-placed Dortmund in the Bundesliga this season, scoring three goals.
