Sports daily said that the scandal-hit boss of the French football's governing body told federation executives and his close ones that he would make his decision known at the next executive board meeting.
The 81-year-old stepped back from his duties in January after a government-mandated audit of his management practices accused him of moral and sexual harassment.
Le Graet is under an investigation by Paris prosecutors for sexist remarks and sexual violence following accusations made against him in 2014 by French football agent Sonia Souid. He denies any wrongdoing.
The football boss, who has led the federation for the past decade and served as vice president from 2005-2011, came under fire in January after making disparaging remarks about French football star Zinedine Zidane. He later apologized.