The Hoops are expected to lose wantaway defender Dedryck Boyata before the end of the month.
Boyata's expected departure would leave the Scottish giants short of options in central defence, and according to Bild, Celtic boss Brendan Rodgers is interested in a deal for Bruma.
Bruma has previously worked under Rodgers in the youth system at Chelsea, and the 26-year-old has formed a solid career since leaving the Blues for PSV Eindhoven in 2013.
The report claims that Celtic are prepared to pay around £7m to land the Netherlands international before the end of the month.
Bruma made four Premier League appearances during his time at Chelsea.