The 21-year old Dutch centre-back has impressed on loan with German club Hamburg over the past two seasons and is now in talks with PSV via representative Jan de Visser.
"It was a first meeting. We will listen to each other," de Visser told Voetbal international.
"I expect there are other sides interested as well but we are curious about the plans for next season."
Bruma has a season remaining on his Stamford Bridge deal but could be on his way out the exit door this summer if an opportunity to play regular football pops up.