Odegbami said his declaration for the FIFA presidency was borne out of the thought that it is high time the world football governing body was led by an African. He formally announced his aspiration on Wednesday, Xinhua news agency reported.
"The choice of an African, specifically a Nigerian, may look far-fetched in this pursuit. I see myself fitting into this role," said the former international football star, nicknamed "Mathematical Odegbami" in his hey day.
He is the second Nigerian who has declared interest in the office of the FIFA president following a declaration earlier made by Orji Uzor Kalu, a former governor of Nigeria's southeastern state of Abia.
Odegbami said he hopes, following his declaration, he will get the necessary support from the Nigeria Football Federation to make his dream of leading FIFA a reality.
The 111-year-old FIFA will hold its next presidential election on February 26, 2016.