The 22-year-old is yet to make a senior appearance for the Citizens since joining the club in 2020, and has instead gained first-team experience out on loan with Braga and Girona.
Couto spent a year with La Liga club Girona and a year in Portugal with Braga before returning to the former on a temporary basis for the 2023-24 campaign.
The four-cap Brazil international starred for a Girona side that surprisingly secured a top-three finish in La Liga to qualify for next season's Champions League, registering eight assists in 34 league matches at right-back.
Couto is now facing an uncertain future at Man City, as it is unknown as to whether manager Pep Guardiola has plans to integrate the youngster into his first-team squad for the new season.
The Coritiba academy graduate has just a year left on his contract at the Etihad Stadium and has not been selected in Man City's initial squad for their pre-season tour of the United States.
Dortmund in talks with Man City over Couto deal
According to the Daily Mail, Man City are now hoping to make a healthy profit on Couto, who cost the Citizens just £5m four years ago.
The report adds that Guardiola's side are in talks to sell the defender to Borussia Dortmund and expect the Bundesliga outfit to table an official bid of around £25m.
It remains to be seen whether Man City will view that offer as an acceptable one, as it has previously been reported that the Citizens could demand as much as £40m for the youngster.
A number of European clubs including Juventus and Bayer Leverkusen have also been credited with an interest in Couto, but Dortmund is believed to be the most likely destination for the right-back.
The potential arrival of Couto at BVB, now managed by Nuri Sahin, could see the Brazilian compete with Julian Ryerson and Marius Wolf for regular starts on the right side of defence.
Dortmund could also explore the market for a new left-back this summer now that Ian Maatsen's loan spell from Chelsea is over, with the 22-year-old opting to join Aston Villa on a permanent basis.