The Football Association submitted a provisional 35-man squad to FIFA on Monday, although they asked for it to remain secret ahead of Southgate's final squad announcement.
The Three Lions coach has preferred Manchester City's player, Fabian Delph who was impressive this season.
Wilshere has missed out after being called up for the friendlies against Italy and the Netherlands in March only to withdraw because of injury.
Hart, 31, had been expected to travel to Russian Federation as third-choice keeper behind Jordan Pickford and Jack Butland despite his disappointing season on loan from Manchester City.
Liverpool's Alex Oxlade-Chamberlain was surely one of the "19 or 20" players that Southgate said in March had sealed their place in the 23, only for a season-ending knee injury to increase the manager's midfield headache. He is everything you would hope a senior player would be'.
Early suggestions were that Southgate would opt for the experience of Hart over Pope, but it is now believed the former West Suffolk College student has won the battle to join Jordan Pickford and Jack Butland as the goalkeeping options.
And Hart has paid the price for a hard season.