Zaha has asked world governing body FIFA to allow him to play for the Ivory Coast, which is the country of his birth.
Zaha, capped twice by England, has asked world governing body FIFA to allow him to play for the Ivory Coast, which is the country of his birth.
The 24-year-old has been pictured holding an Ivory Coast shirt with his name on alongside Ivorian Football Federation president Augustin Sidy Diallo and national coach Michel Dussuyer.
"We're still hopeful that we can speak to Wilf," Southgate said of Zaha, who can change allegiance because both of his England caps came in friendlies.
"I saw him at Everton, where he played OK. I saw him at Burnley, where in the second half he was excellent.
"He's certainly somebody that I think has talent, is in a good moment with his club and ideally I'd like to talk to him before he makes that decision.
"I would like to speak with him before we make a decision on whether we are happy to let that happen."
Zaha made his England debut in a 4-2 friendly defeat by Sweden in Stockholm in November 2012 and also played in a 3-2 win over Scotland at Wembley in August 2013.
The former Manchester United player has been capped 13 times by England at under-21 level.
Southgate is also keeping tabs on Ben Woodburn, who became Liverpool's youngest scorer this week by netting against Leeds United in the League Cup at the age of 17 years and 45 days.
Woodburn was born in England, but plays for Wales at youth level and has said he wants to "replicate" the feats of Wales stars Gareth Bale and Aaron Ramsey.
"Ben's a player we've known about for a long time," Southgate told reporters at Wembley.
"He got into Wales's system very, very young. This is a challenge for us now in terms of the number of dual-nationality boys we have.
"There's also an ethical debate with the really young ones about how soon we start to run camps because ethically we don't want to get boys in too young, but other countries are going younger and younger.
"Ben is a player whose quality we have certainly recognised over the last couple of years, before he's come on the first-team radar this week."