The 20-year-old attacker, who is co-owned by Siena, is on the verge of completing a move to Stadio Olimpico, with Stefano Antonelli, director of the Artemio Franchi outfit, revealing on Sunday that he expects the transfer to be finalised imminently.
Totti admitted at the weekend that he was relishing the opportunity to play alongside Destro, praise which the Italy Under-21 international has welcomed.
"Totti's remarks? I was very pleased with them," Destro told Sky Sport Italia.
Destro, who was part of Italy's preliminary squad for Euro 2012, also caught the eye of Juventus and AC Milan after scoring 12 goals in Serie A last season for Siena.