Stuart Pearce lost his job after a miserable European Championship in Israel and successor Southgate has yet to call upon three of the eligible players that went to that tournament.
Sunderland forward Wickham and Chelsea's McEachran, on loan at Sheffield Wednesday and Watford respectively, have yet to feature under the new regime, joining Swansea midfielder Shelvey in the cold.
The trio have been overlooked for England's European Championship qualifying campaign to date, but Southgate - whose team takes on San Marino on Tuesday night - insists they are still in his thoughts.
"I have watched all of those," he said. "I was at Derby and saw Connor play for Sheff Wed last week.
"I was at Watford v Leicester the week before to see Josh, so you're always looking to see where they are and how they are progressing.
"The door is always open for people that are playing well and want to be part of it and see this as a big part of their football learning, really.
"We're always looking to improve the quality of the squad and if there are players we think can improve it then anybody with us doesn't quite reach the required level has a challenge on their hands."
Southgate admits that one of the reasons he left out Shelvey was because he thought the midfielder might get called up to Roy Hodgson's senior squad.
He said: "I had a good chat with Jonjo a couple of months ago and at the time he had a lot of European football with Swansea.
"There were a lot of other players and he is one of the older ones. I wasn't convinced he would still be with us come the finals.
"There were a few other players I wanted to have a look at and those guys have done really well.
"That is one I will probably revisit in the New Year because we don't play until March, so I will talk to the player.
"I had a feeling he might be with the seniors anyway, so I didn't want to necessarily pick a player that I didn't think would be with us for very long.
"That has not happened so maybe after Christmas we will review that."