According to BBC Sport, the 24-year-old forward is open to extending his stay in west London, although discussions remain at an early stage and are unlikely to progress quickly.
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Schade has scored three goals in five Premier League appearances this season and started both of Jurgen Klopp's opening two matches as Germany manager.
His current deal expires in 2028, leaving Brentford with less than two years to secure his long-term future.
The attacker initially joined the Bees on loan from Freiburg before completing a permanent £22 million transfer in 2023, which was a club-record fee at the time.