Goalkeeper Hart, England's most experienced player, is thought to have missed the cut for the final 23-man squad heading to Russian Federation next month.
The satisfaction of those officially selected by Southgate at Wednesday's announcement will contrast with the disappointment of those missing out on Russian Federation 2018, with the experienced Hart expected to miss the cut.
But Southgate phoned the 31-year-old on Monday night to inform him he had not made the cut.
Everton's Jordan Pickford and Stoke City's Jack Butland have both jumped ahead of Hart in the matches since then, with the keeper enduring a hard season, losing his place to Adrián at the end of November and only starting 19 league games.
The trio boast just nine caps between them, yet former England defender Rio Ferdinand believes Southgate would be right to leave Hart at home.
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The likes of Harry Kane, Raheem Sterling and Jordan Henderson are all having fine seasons for their respective clubs but Lineker feels Gareth Southgate's side are still short of making a real challenge. Whereas a young kid.
"I can only hope he doesn't lose any of the players he has chosen for when he eventually decides these are the ones I want". I know he has done that, so I am sure he has done all the things that needs to be done.
"In my mind I'm pretty clear on who we're picking and whether that surprises people, I guess, remains to be seen".
"Taking a young kid to go there and experience that I think is a much better way to go".
England have warm-up friendlies against Nigeria at Wembley on June 2 and Costa Rica in Leeds on June 7, ahead of the Group G opener against Tunisia on June 18.