The 22-year-old joined the Citizens from Coritiba in 2020, but he has never made a first-team appearance for the English champions.
Couto has spent the majority of his time at Man City on loan at Girona, although he also represented Braga during the 2021-22 campaign, making 42 appearances.
In total, the right-back has made 95 appearances for Girona, scoring five goals and registering 17 assists in the process.
Last season, the Brazilian scored twice and registered 10 assists in 39 appearances in all competitions for a Girona side that finished third in La Liga to secure Champions League football for the 2024-25 campaign.
Couto 'is heading for Dortmund'
According to journalist Patrick Berger, a full agreement has been reached between the two clubs, with official confirmation expected in the near future.
Couto will allegedly spend the 2024-25 campaign on loan at Dortmund, with the move than becoming permanent for €25m (£21m) next summer.
The Brazilian is said to have agreed a five-year deal with BVB, and he is expected to undergo his medical with the Bundesliga outfit later this week.
Dortmund had allegedly identified Couto as their leading target at right-back and have now been able to come to a full agreement with the English champions.
Should Man City have kept Couto?
Kyle Walker is Man City's first-choice right-back, but the England international will turn 35 next year, so he is very much in the latter stages of his career.
Meanwhile, Joao Cancelo - another of the club's right-backs - is widely expected to leave this summer, with a return to Barcelona likely.
As a result, it is somewhat of a surprise that Man City are willing to let Couto leave considering his form last season.
Indeed, the Brazilian managed one goal and 10 assists in 34 La Liga appearances, with Girona having a historic season, and there were some suggestions that he could be a part of the Man City squad moving forward.
However, he has been allowed to depart, and a fee of €25m (£21m) could turn out to be a bargain for Dortmund considering his quality.