The 22-year-old, whose contract expires in a year's time, was a league winner in each of the past two campaigns and would be a solid addition for most top-flight sides.
But where could he go? Here's a few options...
West Ham United
Carl Jenkinson's injury - and subsequent return to Arsenal - often saw Slaven Bilic shunt winger Michail Antonio to right-back. With Joey O'Brien gone too, only Sam Byram remains, and Brenet, who can also play on the left, would not only provide the former Leeds man with competition, but Aaron Cresswell too.
According to ESPN, the Mackems may look to bring last season's loan star DeAndre Yedlin back to the North East from Tottenham Hotspur. Brenet, though, would be a perfectly adequate replacement should a move for the American fail to materialise. With fellow Dutchmen Patrick van Aanholt and Jeremain Lens for company, the youngster may be keen.
The Toffees are parting ways with long servant Tony Hibbert this summer and new boss Ronald Koeman may seek to replace him, depending on what he decides to do with youngster Jonjoe Kenny. Again, the Dutch connection could swing it, though the presence of Seamus Coleman is likely to limit Brenet's first-team chances.
Leicester City and Middlesbrough could both be in the market for right-backs, though much will depend on the future of Ritchie de Laet, who's been on loan to Boro from the Premier League champions.
However, one place Brenet perhaps won't be going is Manchester United, where his once training ground foe Memphis Depay currently plays.