The 61-year-old, who sold the Championship side in May after three tumultuous years in charge, has made an offer to acquire the financially-troubled Italian club for around £5.8m.
Brescia CEO Aldo Ghirardi is quoted by Ansa as saying: "We are ready to accept Cellino's offer and hope it is the right choice. Over the next few days we will formalise everything."
Located in the north of Italy, Brescia last played in Serie A six years ago and last season managed a 14th-place finish in the second tier.
Prior to his acquisition of Leeds, Cellino served as president of Cagliari from 1992 to 2014.