West Brom blew PSV Eindhoven out of the race to sign Bruma from Galatasaray with a £16m-plus bid, according to reports in Turkey.
But the talented Portuguese winger remained in Istanbul and is now the subject of interest from Arsenal, Tottenham and Manchester United.
Spor HD claim PSV technical director Marcel Brands made a £6.25million bid for the former Sporting Lisbon starlet - only for Albion to more than double that offer just before the transfer deadline.
Galatasaray decided to refuse the bid and believe they made the right decision given Bruma's impressive form this season for the club - and the Portuguese Under-21 side.
The 21-year-old has scored twice in six matches for the Turkish club this season and set up a handful of goals for his team-mates in Portugal Under-21s' 7-1 win in Liechtenstein on Tuesday.