The 21-year-old has been scouted extensively by Spurs, and the report claims Feyenoord value the centre-back at £5.5m.
Bruno can operate at left-back or centre-back, and has impressed at the heart of the Feyenoord defence this season.
The Portuguese-born defender has won seven caps for Netherlands, scoring two goals after progressing through the youth national team ranks.
Feyenoord currently sit third in the Eredivisie and much could depend on their eventual league finishing position - depending on European qualification.
And the Dutchman is not the only summer transfer target for Spurs, according to the report.
Andre Villas-Boas remains a huge fan of Internacional striker Leandro Damiao, and is likely to return with another bid for the Brazilian at the end of the season.
But if Tottenham and Internacional fail to reach an agreement again, Villas-Boas could turn to Braga forward Eder.
Villas-Boas managed the 25-year-old striker when both were at Portuguese club Academica, and Eder has impressed for Braga in the Champions League group stage this term.
Spurs recorded a crucial 2-1 win over north London rivals Arsenal on Sunday, sending them into third place and into pole position to secure a Champions League qualification spot.