"Boards of KPN concluded that both approaches fail to provide tangible and material added value over KPN's recently updated growth strategy," the company said in a statement.
It said there had been no discussions or negotiations with EQT, Stonepeak or KKR, adding that the EQT-Stonepeak proposition did not include an offer price.
In April, the Wall Street Journal reported that private investors, including EQT, sought to pay 3 euros per share for the top Dutch telecoms provider.
The consortium is considering whether to raise its offer, the Financial Times, which first reported on the bid, said on Sunday.
Addressing an earnings conference on Friday, KPN's Chief Executive Officer Joost Farwerck said the company was investing in infrastructure for the first time in 26 years and is not seeking to be bought.
Both EQT and Stonepeak have been circling KPN since last year and started conducting due diligence last month, the FT reported, citing multiple people with direct knowledge of the talks.
EQT declined to comment, Stonepeak did not immediately respond to Reuters' request for a comment on Sunday.
Any deal could also be opposed by the Dutch government, which through a law adopted last year, has the option to block takeovers of Dutch telecom companies if they are deemed a threat to national security.
KPN also has a defence against unwanted takeovers in the form of a foundation that can build up a controlling stake to block any deal.
This proved successful in 2013, when KPN won a lengthy battle against unsolicited interest from Mexico's America Movil.
($1 = 0.8321 euros)
(Reporting by Aishwarya Nair and Anirudh Saligrama in Bengaluru; Editing by Alex Richardson and Barbara Lewis)
