Sunderland striker Fabio Borini is undergoing a medical at AC Milan ahead of a return to Serie A.
Maxime Gonalons is close to leaving Lyon and joining Roma, the France international's agent has announced.
Allegri and Barzagli were teammates at Pistoiese in 2000 when Allegri noticed that his colleague was not playing to his strengths.
Inter have made an offer for 16-year-old Pellegri, who scored his first Serie A goal on the final day of last season, and 15-year-old Salcedo.
Totti brought an end to his 25-year career with Roma at the end of the season.
Roma have completed the signing of full-back Rick Karsdorp from Feyenoord, with the 22-year-old signing a five-year contract with the Giallorossi.