According to the Spanish newspaper AS, the Switzerland international is on Real Madrid's radar if talks over a contract extension with current number one Thibaut Courtois, whose deal runs until 2027, break down.
Kobel had already been offered to the Madrid club in the past, so the Blancos' decision-makers are keeping a close eye on the 28-year-old's situation.
At Borussia Dortmund, Kobel is under contract until 30 June 2028. Most recently, Sport Bild reported that BVB are desperate to keep working with the Swiss goalkeeper and want to extend his deal early.
Under coach Niko Kovac, the 28-year-old has been the undisputed number one for years and has made 221 competitive appearances for the Black and Yellows overall, conceding 282 goals and keeping 72 clean sheets.
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Will Gregor Kobel extend his contract at BVB?
How interested Kobel is in extending his contract in Dortmund remains unclear. In the past, rumours regularly linked him with Europe's top clubs, and FC Bayern Munich were at times said to view the Swiss as a potential successor to Manuel Neuer.
That move to Säbener Straße has long been off the table, though, with the German record champions now having found their crown prince in Jonas Urbig. Kobel is still said to be highly rated by several Premier League clubs.