The 24-year-old asked to leave on a temporary basis in the summer when it became clear he would not be a regular in Wenger's first team despite returning to fitness after missing the majority of the previous two years through injury.
Bournemouth ended up taking him to the Vitality Stadium for the season and he has flourished to the extent that he returned to the England squad for the recent double-header against Scotland and Spain.
The Cherries visit Arsenal on Sunday with Premier League rules stipulating Wilshere will not be allowed to play against his parent club, having played in the last seven games for Eddie Howe's side.
Wenger has allowed Wilshere to go about his business on the south coast but revealed the academy graduate, whose current deal expires in the summer of 2018, will be offered fresh terms after the festive period.
Asked if he wanted to extend Wilshere's stay at Arsenal, Wenger replied: "Yes, of course.
"We have to plan that around the new year
I think it was basically in the end a big decision for him to go.
"He gets regular football and now on the observations I get from our people who watch him, he's getting stronger every week.
"That's exactly what he needed - to have regular football, maybe not every three days but every week at the start
That has helped him a lot to develop and come back to the level he deserves to be at."
Wenger said he had not spoken to Wilshere since his temporary departure and was not worried when he heard the player was hoping for Bournemouth to run out the winners on Sunday lunchtime.
"Not since he left," the Frenchman replied when asked how often he speaks to Wilshere.
"I leave him to deal with his manager
Every week I ask, 'How did he play?', I read the reports and when I can see highlights or watch him on television, I will watch him.
"I'm happy that he hasn't had any injuries since he left us.
"That (wanting Bournemouth to win) is normal when you're committed to a club
When you sign for a club you are committed to a project and you have to do well in that season.
"You can't say you want your own team to lose the game."
While Wilshere was concerned about the number of midfielders in front of him in the pecking order, Wenger has been having to make do without the influential Santi Cazorla.
The Spain international injured his Achilles in the 6-0 win over Ludogorets last month and there is still no date set on his return.
"He's important to our technical stability in the team, to the quality of our decision making and to our build-up from deep midfield to the high midfield," Wenger said of Cazorla.
"That's an important stage because it gets the ball out from the defenders
We have enough quality players in our side to get around that, even if Santi is a massive player for us."
With Cazorla sidelined, Wenger has played Francis Coquelin with Granit Xhaka, Mohamed Elneny and Aaron Ramsey in the last three games.
Some Arsenal fans have been perplexed by the lack of opportunities handed to Xhaka, who signed for over £30million in the summer.
The 24-year-old Switzerland international has started just five Premier League games but Wenger insists he is pleased with the progression of the former Borussia Monchengladbach man.
"I'm very happy with his commitment," he said.
"I think he's developing well
He hasn't maybe started enough since the start of the season but he is adapting to a different league, a different way of playing.
"Overall I'm happy because every day he's focused on working hard and I'm confident he'll get his number of games."
Source : PA
Source: PA