PSV are reportedly hoping to sign Bruma from Galatasaray, the winger having also recently caught the attention of Manchester United boss Jose Mourinho.
According to the Milliyet newspaper, the Eredivisie champions will be increasing their initial €6 million bid to one of €8m after the 21-year-old told them he was happy in Turkey.
Bruma, who arrived at Gala for €10n from Sporting CP in 2013, has netted five times in six pre-season friendlies, including a goal in the 3-2 defeat to United.
It was a performance believed to have impressed Mourinho, who according to compatriot Bruma, spoke to him after the game.
"He [Mourinho] congratulated me for the performance and said he was impressed with me. He promised to closely monitor my work and said I could play for the national team soon," the Portuguese attacker said.
"Of course it was amazing to hear this from Mourinho and he said he will keep an eye on how I do this season."
While Mourinho's comments have fuelled speculation that the FA Cup champions are also eyeing Bruma, Galatasaray are said to be wanting in the region of €25m for his services, far above PSV's supposed offer.