The Denmark international has made eight first-team appearances for United but has found game time hard to come by in the Premier League.
Manchester United are yet to make a final decision on whether to loan Obi out, but the option remains on the table.
Any move will depend on the right club being available, along with how pre-season develops for the 18-year-old.
Transfer journalist Pete O'Rourke has reported that United previously held talks with Cologne over a loan deal for Obi.
Bold's own reporting confirms there has been German interest in the striker, though there has been no direct contact between the two clubs.
Several enquiries have been made about Obi in general, but nothing has developed into anything concrete so far, according to the report.
Obi joined United from Arsenal in 2024 after turning down a first professional contract with the Gunners.
He made a strong impression during his first season at Old Trafford, becoming the youngest player to start a Premier League game for the club when he featured against Brentford in May 2025.
However, last season saw his involvement limited almost entirely to youth-team football.
Obi has represented Denmark at various youth levels and was named the Comet of the Year by Bold in recognition of his rapid progress since arriving in England.
He famously scored 38 goals in 25 games during a record-breaking Under-18 Premier League campaign in 2024.
A loan would give Obi the chance to gain senior experience away from Old Trafford, with United still weighing up whether that route is the right one for his development.