Roma want to get Pastore’s €3.5m-a-season salary off their books and he is being offered to clubs.
Two sides from Saudi Arabia have shown interest in the former Paris Saint-Germain star.
A move to the Middle East or America would guarantee Pastore, 31, a big salary.
However, Zenit could provide Champions League football to the 29-cap Argentine international.
Pastore made only 11 league appearances for Roma this season and was an unused sub in their last eight games.
Roma paid €24.7m to sign Pastore from PSG two years ago but his market value has dropped to around €8m.