Manchester United goalkeeper Dean Henderson is on England's radar.
Southgate said: “I'm not prepared to pick players just to stop the possibility of other countries picking them. Aaron Wan-Bissaka is playing really well and he's one that is really pushing to be in our squad, without question.
“I could pick players and give them a cap to stop them playing for someone else but I don't think that's right.
“In terms of Angus (Gunn), he's just got into the team – so Alex McCarthy is unfortunate to be out of the team at Southampton – and Angus has got a good challenge to get in our under-21s because Dean Henderson is playing really well at Sheffield United and is also close to our squad.
“There's good competition for places."