After a spell back in Argentina the attacking midfielder joined Panthinaikos, signing a contract that expires after the end of the current season.
Gershon, 28, is captain of the Israeli national team and could join fellow countryman Tal Ben Haim if he can clinch a deal.
Allardyce sent scouts to watch Gershon in action for Hapoel Tel Aviv yesterday and with the player out of contract in the summer, is hoping to land him for a small fee early next week.