The late singer died on 16 August, aged 76, after suffering from pancreatic cancer.
According to court papers obtained by celebrity news website TMZ, she died "intestate," which means she did not have a will.
Her four sons, Clarence, Edward, Ted and Kecalf, will have equal shares in her estate according to Michigan law, the website reported.
Franklin's net worth is estimated to be around $80m (£62m), according to celebritynetworth.com.
Her finances will soon become public in Oakland County Probate Court since she left no will or trust, Detroit Free Press claimed.
Franklin's niece, Sabrina Owens, allegedly asked the court to appoint her as personal representative of the estate.
The 18-time Grammy Award winner had suffered ill health for many years, having surgery in 2010 for an undisclosed tumour.
She also cancelled a series of concerts in 2017 for health reasons.
"In one of the darkest moments of our lives, we are not able to find the appropriate words to express the pain in our heart," Franklin's family said in a statement following her death.
"We have lost the matriarch and rock of our family.
"The love she had for her children, grandchildren, nieces, nephews, and cousins knew no bounds."
Her publicist, Gwendolyn Quinn, said that her funeral will be held at Greater Grace Temple in her hometown of Detroit on 31 August and will be limited to her family and friends.
The multiple-day celebration of her life will begin with an open casket memorial at the Charles H Wright Museum of African American History.
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Franklin's death prompted an outpouring of tributes from countless celebrities, politicians and prominent figures in American life, including Barack and Michelle Obama.
"Every time she sang, we were all graved with a glimpse of the divine," they said of her.