He was not called up to the most recent squad for this week's match with Germany despite a couple of dropouts and now, manager Gareth Southgate has explained why.
With time running out for the 25-year-old to clinch a place in the Southgate's squad, a former England manager is set to hand him a lifeline.
With his England exile showing no signs of ending and Wenger's midfield pecking order well established, reports have suggested that Wilshere may have to leave Arsenal in January in order to keep alive his hopes of earning a place in England's squad for the 2018 World Cup in Russian Federation.
Wilshere has found his opportunities limited at Arsenal this season after spending last season out on loan at Bournemouth. But we are not playing with a 10 tomorrow.
"We have never mentioned his name".
"But I want to be clear, I really like Jack Wilshere as a player".
West Ham United, Swansea City and La Liga outfit Real Betis are all said to be monitoring the player's situation, while The Telegraph recently claimed that struggling Palace were prepared to offer him a lifeline.
Home-grown Adams feels that was an important part of the Arsenal side that famously won the league in 1989, with the likes of David Rocastle, Michael Thomas, Paul Davis, Niall Quinn and Paul Merson all also having emerged from the club's youth team.
Jack Wilshere has won 34 caps for England, including in the Federation Internationale de Football Association 2014 World Cup. That's what you need to find out, because it didn't come from us.
"I think he is a deeper player but he is not playing deeper".
"I've been here 10 years, I love this club and feel like I have a special relationship with the fans", Wilshere told Standard Sport.
"It is alright Arsene Wenger saying a fit Jack Wilshere gets in the England team, but you have to play for Arsenal".