The reigning Turkish champions are keen to lure the promising youngster to Istanbul and have started formal negotiations with his current club
The Turkish champions are keen to add some fresh blood to their attack before the summer transfer window closes on Wednesday and they see the 18-year-old Bruma as the ideal addition to their squad.
"Galatasaray announce that formal negotiations have been opened with Sporting CP over the transfer of Armindo Tue Na Bangna [Bruma]," a statement on Galatasaray's official website reads.
Bruma is a product of the renowned Sporting youth academy, producing players such as Cristiano Ronaldo and Nani, and made his official first team debut last term.
The winger was one of the stars of this summer's Under-20 World Cup, netting five goals in four games for Portugal.
His current contract with Sporting is due to expire in the summer of 2014.