A private family funeral was held for Mr Dexter last week after he died in March at the age of 86.
Chairman of the Inspector Morse Society, Dr Antony Richards, who was a friend of the author, said he expected a memorial service to take place in a few months’ time.
He added: “Ted Childs, the original executive producer of the Inspector Morse episodes, is hopeful that there will be some sort of service in London.
“I think it would be very fitting if there was also a service in Oxford.”
Filming began this week for the fifth series of Endeavour, which will be broadcast on ITV next year.
Executive producer Damien Timmer said: “It was a privilege to work with Colin on Endeavour and everyone involved will miss his contribution to the show.
“He was the most delightful collaborator with a razor-sharp mind.
“We hope this new series will continue to do his legacy justice.”
Mr Dexter kept up his tradition of making cameo appearances until the most recent series of Endeavour, when he was instead represented by a portrait on the wall of the Oxford Mail newsroom.
The next series will have six feature-lengths films, once again starring Shaun Evans as the recently promoted Detective Sergeant Endeavour Morse.
Roger Allam returns as DI Fred Thursday while Anton Lesser and Dakota Blue Richards also reprise their roles.
The drama, penned by series creator Russell Lewis, begins with Morse having finally passed his sergeant’s exams as Oxford City Police merges into Thames Valley Constabulary.
Filming is set to return to the city, where university colleges and city centre streets are regularly used to allow crews to have backdrops which have not changed since the late 1960s, when the prequel series is set.