The Germany international has made an impressive start to the season, scoring three goals as Brentford remained unbeaten through their opening five Premier League matches.
Arsenal and Liverpool are understood to have been among the clubs most interested in Schade towards the end of the summer transfer window, while Chelsea and Tottenham have also previously monitored the winger.
Schade joined Brentford from Freiburg for £20 million in June 2023 and has entered the final two years of his current contract.
The West London club are now looking to improve his terms and extend his stay as his importance to the team continues to grow.
The 24-year-old has scored 25 goals and provided nine assists in 119 appearances for Brentford since his move to England.
His form has also strengthened his position with Germany, with Schade starting Jürgen Klopp’s first match as national team head coach in the 1-1 draw with the Netherlands.
Brentford’s decision to begin contract talks comes with the club sitting fourth in the Premier League after five matches, having recorded victories over Tottenham and Chelsea alongside three draws.
The club will now look to reach an agreement with Schade before interest from elsewhere develops further.
Arsenal and Liverpool have not made a formal offer, but Brentford’s decision to open negotiations reflects the growing importance of keeping the winger at the Gtech Community Stadium.