According to BILD, all three Premier League clubs have registered serious interest in the 20-year-old Ivorian, who enjoyed a breakout campaign on the German club's left flank.
Touré scored five goals and provided nine assists in 30 Bundesliga appearances as Hoffenheim secured a top-five finish and Europa League qualification.
That return, allied to his pace and direct running, has made him one of the most heavily scouted wide players in Europe this summer, with reports suggesting Liverpool and Aston Villa are also monitoring his situation.
Hoffenheim's negotiating position is strong. Touré signed a contract running until 2029 when he joined from Swedish side Hammarby in January 2025, and that deal contains no release clause.
Sporting director Andreas Schicker has made clear that Hoffenheim are under no pressure to sell, though the scale of interest from England suggests a significant offer could still force the issue.
Reports in Germany have placed Touré's valuation in the region of €40million to €50million, a figure that would represent a substantial profit on the modest fee Hoffenheim paid for him just 18 months ago.
For Manchester United, the interest in Touré comes as the club continues to assess its options across the forward line ahead of a summer that is expected to bring further changes to Michael Carrick's squad.
Newcastle United, by contrast, have reportedly already done groundwork on personal terms, with scouts dispatched to watch Touré in person on multiple occasions in recent months.
Brentford's interest is consistent with the west London club's recruitment approach in recent windows, where they have repeatedly identified promising Bundesliga talent before prices climb out of reach.
Whether Brentford can compete financially with United and Newcastle for a player valued at up to £43million remains to be seen, particularly with several other Premier League clubs believed to be aware of the situation.
Touré is currently away with Ivory Coast's World Cup squad, where he is set to feature alongside several players already familiar to Premier League scouts.
A tournament with a heavy spotlight on young, attacking talent could only add to the queue of suitors, with Hoffenheim braced for offers to arrive once the group stages are underway.
For now, Touré remains a Hoffenheim player with three years left on his contract, giving the Bundesliga club every incentive to hold out for their asking price, whoever ends up making the move.