Brobbey, 24, joined Sunderland from Ajax last summer for around €20m and scored 7 goals across all competitions in a debut Premier League season that helped the newly promoted club finish seventh and qualify for the Europa League.
His performances in North America — including a brace in a convincing win over Sweden — have significantly raised his profile further among clubs across Europe and England.
According to journalist Graeme Bailey, Atletico Madrid are monitoring Brobbey as a potential replacement for Julián Álvarez, who publicly called for a transfer at the weekend.
Manchester United are also long-standing admirers and are seeking a striker to partner or compete with Benjamin Sesko. Tottenham and Chelsea are named as additional Premier League suitors, with Juventus, Stuttgart and Aston Villa completing a broad list of interested parties.
Sunderland are making clear they have no intention of selling. The club view Brobbey as central to their long-term project and have not attached an asking price to the Dutch international. He is contracted to the Stadium of Light until 2029 and internal discussions over a new deal have already been held at boardroom level.
Brobbey arrived at Wearside with his confidence dented after a difficult final season at Ajax but flourished under manager Régis Le Bris, combining pace, physicality and a high-pressing game that proved effective both in Sunderland's promotion push and in their remarkable first season back in the Premier League.
Whether Sunderland can resist the pressure of multiple elite clubs remains to be seen, but for now their stance is unequivocal.