Southgate will name his 23-man squad for the summer tournament today and looks set to omit the three high-profile figures.
The experienced Hart expected misses the cut, and reports last night said Arsenal midfielder Wilshere has also been told he will not be travelling, with the same applying for Chelsea defender Cahill.
Wilshere has not played for his country since the Euro 2016 exit to Iceland but was in line to start against Holland in March before injury put his World Cup hopes in jeopardy.
Manchester City’s versatile Fabian Delph is said to have been included by Southgate, with Burnley centre-back James Tarkowski part of the group on standby.
With Hart missing out, uncapped Burnley goalkeeper Nick Pope could get the nod alongside Jordan Pickford and Jack Butland. The trio boast just nine caps between them, yet former England defender Rio Ferdinand believes Southgate would be right to leave Hart at home.
“It’s the right decision,” Ferdinand said at the BBC’s launch of its World Cup coverage.
“What is Joe Hart going to learn from going to this World Cup? What is Gareth Southgate going to learn about him? Whereas a young kid...
“I went to the World Cup in ’98, didn’t play one minute of football, but it was a great learning curve for me.
“When I went to the next World Cup and played in 2002, I didn’t have anything I needed to learn... taking a young kid to go there and experience that I think is a much better way to go.”
Uncapped Liverpool defender Trent Alexander-Arnold’s promising campaign has put him in with a shout, and Southgate may consider the likes of Chris Smalling and Michael Keane to bolster his centre-back options.
In midfield, Newcastle’s Jonjo Shelvey has performed well recently but last donned the Three Lions in November 2015.
Adam Lallana, England’s player of the year in 2016, is a fitness doubt, although Ruben Loftus-Cheek is an exciting option.
Although the world governing body does not need it whittled down until June 4, Southgate will name 23 players to strip unnecessary anxiety and pressure from preparations.
England’s Group G opener is against Tunisia on June 18.