A KPN spokeswoman said the company would not comment on "rumours". EQT declined to comment.
A report in the Wall Street Journal cited people familiar with the matter that EQT might seek to pay 3 euros ($3.56) per share for KPN this spring, working together with New York-based Stonepeak Infrastructure partners.
EQT was named in stories by Reuters and Bloomberg in 2020 as weighing a bid for KPN, whose shares were up 1.6% to 2.92 euros by 0721 GMT on Thursday.
KPN has indicated it does not wish to be bought and has a poison pill mechanism in place to thwart unwanted takeovers, whereby an independent panel can issue new shares, as it did to block a takeover attempt in 2013.
Its networks were identified as infrastructure critical to national safety under a law that went into force in October 2020 giving the government the right to veto a takeover.
America Movil owns a 20% stake in KPN.
The company entered a joint venture with pension fund giant ABP to build fibre optic networks last month and owns some fibre optic networks in southern Netherlands and Belgium.
($1 = 0.8424 euros)
(Reporting by Toby Sterling and Supantha Mukherjee; editing by Jason Neely)