Argentina centre-back Silvestre is reportedly just a few steps away from completing an 11million euros transfer from Palermo to Inter.
Inter are also in the race to acquire Destro, who is co-owned by Siena and Genoa.
"Destro and Silvestre are two players worthy of wearing the Inter colours," Zanetti said to Corriere dello Sport. "They would strengthen our side."
Argentina striker Rodrigo Palacio is the only acquisition made by the Nerazzurri outfit so far, with the Argentinian striker having joined Inter on a permanent transfer from Genoa.
Zanetti knows Inter have to strengthen their squad this summer if they are to compete for the league title next year.
Inter finished a disappointing sixth this season.
"As it is right now there are teams that are better equipped than us for the scudetto," Zanetti said.