Hiddink has endured a tough start to his reign since replacing Louis van Gaal in the summer as the Dutch have lost two of their three Euro 2016 qualifiers.
The 67-year-old was named as Van Gaal's successor as early as March, and Gullit has criticised the KNVB for overlooking Koeman - now Southampton boss - for the position.
"The association passed up the opportunity to rejuvenate the team", Gullit wrote in De Telegraaf. "I would have opted for Koeman.
"This generation of players know him. I do not understand why the association chose Hiddink. It was a cowardly decision and I put the blame on the KNVB."
The Netherlands sit third in Group A, six points behind co-leaders Iceland and Czech Republic.