Known as White O'Morn in the 1952 film, the privately owned building in Connemara, County Galway, has been derelict since the 1980's.
Each year, thousands of fans flock to the locations in County Mayo and County Galway where the film was made.
Many have taken stones from the cottage as souvenirs, adding to the dilapidation.
A visitor once boasted that every stone in her fireplace had come from the Quiet Man cottage.
Protected status will make the removal of stones and other items illegal.
In the movie, directed by John Ford, retired American boxer Sean Thornton (John Wayne) returns to the village where he was born and falls in love with Mary Kate Danaher (Maureen O'Hara).
The scene in which Wayne kisses O'Hara at the door of the thatched cottage is one of the most famous in the history of film.
The Quiet Man cottage was an historic family home dating back to the pre-1820s.
A local family were still living there at the time the movie was made.  Only exterior shots were filmed in Ireland. All interiors were shot in Hollywood.
Records show the cottage existed on the same site as far back as 1820.
It is expected the council will announce its decision in July.
Campaigners have been appealing for protected status and restoration of the building for almost 20 years.
An online petition was immediately signed by star of the film, Maureen O'Hara.
To date almost 9,000 people have signed it.
Speaking in 2014, the actress said: "If you think about Duke, John Ford and all the people who worked on the picture, it is sad to see the cottage in shambles.
"How can anyone say anything but wonderful things about it, and see to it that it is restored for them and in their memory - and for Ireland."
A cottage made famous in movie The Quiet Man could be listed as a building with protected status.