Wilshere put seasons of injury woe behind him last term after making 38 appearances in all competitions for Arsenal, seemingly putting him the frame for a place on board the plane to Russia.
The midfielder was left out of Southgate’s final squad however, with Jordan Henderson, Eric Dier, Fabian Delph and Ruben Loftus-Cheek selected ahead of him.
Wilshere joined West Ham this summer with his first-team prospects improving before injury struck again in October.
The 26-year-old had hoped to be back in international selection for England’s Nations Cup campaign but is yet to hear from his manager since his summer snub.
“No, I haven’t heard from [Southgate],” Wilshere told BTSport.com
“But as a footballer and as an English player playing in England, the day that you say you don’t want to play for your national team or give up, is the day you should really give up playing football.”