The actor, who played Richard 'Boner' Stabone in the 1980s sitcom, was found dead in a Vancouver park last week after he was reported missing on February 16.
According to E! News, a source close to his relatives has revealed that a service will take place "fairly soon", but that guests have been asked to keep the details private.
The 41-year-old's family have previously said that they "appreciate" the support and well-wishes that they have received. They also claimed that they are planning to create a "remembrance book" containing fans' letters and emails.
Koenig's former co-stars Kirk Cameron, Tracey Gold and Alan Thicke are among the stars who have publicly paid tribute to him.