Gareth will reveal his 23-man squad on Wednesday.
Wilshere has not played a single minute under Southgate since former England defender took charge on the Three Lions - initially on an interim basis - in September 2016.
Yet, his performances at the end of the season forced Southgate to consider Wilshere for a place on the plane to Russian Federation.
As announced by the Guardian, the 26-year-old has been excluded from the squad following a below par season in which he managed just 12 Premier League starts.More news: Union Cabinet reshuffle: Goyal gets finance portfolio; Smriti out of I&B Ministry
Doubts over his possible selection have also intensified due to the impressive performances of Burnley goalkeeper Nick Pope, Everton's Jordan Pickford and Stoke's Jack Butland, and it now appears that Hart himself has had the news confirmed to him.
Former West Suffolk College pupil Pope was named in Southgate's squad for friendlies with Holland and Italy in March, but didn't see any playing time, making the World Cup pick all the more remarkable.
"Taking a young kid to go there and experience that I think is a much better way to go". He is everything you would hope a senior player would be'.
The news bodes well for Burnley's uncapped keeper Nick Pope who now looks to be in prime position to be named in the squad which heads for Russian Federation on Tuesday, June 12.