Aston Villa are understood to have explored the possibility of signing Min-jae during the summer, although no transfer materialised.
The centre-back remains under contract with Bayern for another two years, but uncertainty surrounding his long-term future could create an opportunity next summer.
According to Bild football chief Christian Falk, Villa remain interested and could return for the defender in 2027.
“They already had him on their radar in the summer,” Falk said.
“They had already looked into him and made enquiries. It didn't happen then. But he's a topic again for next summer.”
Min-jae joined Bayern from Napoli in the summer of 2023 and has made more than 70 appearances for the German club.
His current position is less straightforward, however, with the 29-year-old not currently an automatic starter.
He has made five Bundesliga appearances this season, with his most recent appearance coming in Bayern's 7-0 victory over Union Berlin earlier this month.
The defender has reportedly remained happy in Munich despite the competition for places.
Villa's interest would nevertheless give Bayern another factor to consider as they assess Min-jae's future.
If the South Korean remains without a regular starting role and enters the final year of his contract next summer, Bayern could potentially face a decision over whether to sell or attempt to extend his agreement.
Villa have already demonstrated an interest in adding experienced defensive options, and Min-jae's combination of Champions League experience and Premier League familiarity could make him an attractive target.
The South Korean also has experience of English football from his time at Tottenham?
For Villa, however, any potential deal remains dependent on Bayern's position and the player's contract situation.
Min-jae even scored against Villa during a pre-season friendly this summer, adding an unusual connection between the defender and the club now reportedly tracking him.
For the moment, the interest remains at the monitoring and enquiry stage.
But according to Falk, Villa have not forgotten about the Bayern defender and could revisit the possibility of a move next summer.