His early work used dub poetry, a Jamaican style that evolved into the music genre of the same name.
Zephaniah was also an actor and appeared in the BBC drama series Peaky Blinders, set in Birmingham, between 2013 and 2022.
Since his death, tributes have included a city centre exhibition and a mural.
“He always saw himself as a ‘son of Birmingham’ and he was passionate about promoting the city”, his brother Tippa Naphtali said in a statement.
Two separate reports recommending the honours for the artists will be discussed at a council meeting on 28 January.