Manchester United striker Wayne Rooney and Liverpool midfielder Jordan Henderson, both absent from the English squad, have previously captained the side under Southgate.
"I guess I am giving myself time to think through what the best scenario (for captaincy) is, really," Southgate told the British media.
"We did that with Gary (Cahill in Germany) - I know he's not playing on Sunday and it is opportunity to share that responsibility.
"I think people have stepped up in their performance, so there were people that weren't wearing the armband that played with the ball as leaders."
The former Middlesbrough boss said goalkeeper Joe Hart could be next in line for the captaincy role but he preferred developing more leaders in the squad.
"It's something I want to think through, but it is not as important to me as making sure there is more development and that more are given responsibility."
England are top of Europe's World Cup qualifying group F having won three of their four games, and are two points clear of second-placed Slovenia.
(Reporting by Hardik Vyas in Bengaluru; editing by Sudipto Ganguly)
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