Zaha announced last month that he intends to switch allegiance to Ivory Coast, the country of his birth, despite having already made two friendly appearances for England during Roy Hodgson's tenure.
But Southgate, who was in the stands at Selhurst Park for Palace's win over Southampton on Saturday, is hopeful that the 24-year-old may reconsider his decision.
"We are still, first and foremost, hopeful that we can speak to Wilf," he said. "He's a player I've worked with at Under-21s level and he has played very well this season.
"I've had a conversation about him with [Palace manager] Alan Pardew and also with Palace chairman Steve Parish.
"He is certainly someone who has the talent, is in a good moment with his club and ideally I'd like to talk to him before he makes that decision final.
"I cannot assess whether he has gone too far down the road until I speak with him."