The 24-year-old is closing in on a return for the Gunners, having not played a competitive game this season after suffering a broken fibula on the eve of the campaign.
Hodgson is a big fan of Wilshere, who also has a history of ankle injuries, and has hinted he would happily take the 28-capped international to France - regardless of if he even manages to make an Arsenal comeback before the end of the season.
And Wenger has given his backing to Wilshere's potential inclusion after announcing he is back in full training.
Asked if taking Wilshere would be a gamble, the Frenchman replied: "If he's completely fit, no.
"When you're a national team coach, you can take a gamble on one player but certainly not on five
He has to consider the whole situation
You can certainly take a chance on just one player."
Some Arsenal fans may be hoping Wilshere does not feature for England given his wretched injury record, but Wenger was unequivocal when answering whether he felt Wilshere would make the squad and if he would welcome his call-up
"Yes
Yes to both questions
Both answers are yes," he said.
When asked whether he would prefer to see Wilshere stay at home, the Gunners boss replied: "You want your players to compete
"When you're a footballer you want to compete at the top level and what is important is that Jack, who is frustrated enough, regains confidence.
"It's very important for his confidence that he can go to the Euros and he can play
It's also important to have a player of his quality available."
Wilshere could play in Arsenal's under-21 clash with Newcastle next Friday, but Wenger will keep a close eye on his developments before including him in the first team.
"I'm cautious with him now but, to be back fully competitive, it will take a few weeks," he added.
"Once he will be completely fit and competitive, he will be available for Arsenal and for the national team
Why not?"
Source : PA
Source: PA