Southgate is understood to believe that Pope's form and ability outweigh Hart's experience, with the England manager placing little value on a player's involvement in major tournaments.
Hart, a veteran with 75 caps, started just 19 of West Ham's Premier League fixtures this season after losing his place to Adrian under David Moyes.
Pope has been sensational since making his Premier League debut after Tom Heaton picked up an injury.
Southgate submitted a 35-man preliminary list for his World Cup names on Monday, with the final 23-man selection to be announced on Wednesday.
England face Nigeria at Wembley Stadium on June 2 in a pre-tournament friendly, before playing Costa Rica at Elland Road on June 7.
Their delight will contrast markedly with the disappointment of those missing out, with Hart - comfortably England's most experienced player - said to have missed the cut.
"I would have him [Shelvey] in my squad", Shearer said on Sunday's Match of the Day. We have also come off the back of two nil-nils against Brazil and Germany so in terms of our defence and our goalkeepers they have had as good performances as anybody in Europe up to this point.
"We had the best defensive record in Europe". Three types of goalkeeper in as many ways - in terms of their experiences and styles.
"If we play tomorrow, I think Joe Hart would be our number one".
"For any coach, it is the most hard conversation because any time you pick a team and leave a player out. having been a player, I know how upsetting that is", he said.