The 24-year-old moved to the Emirates Stadium in May as the Gunners' third-most expensive signing in their history.
Xhaka returns to home-town club Basle in the Champions League on Tuesday night and is expected to start for Arsenal against the team where he began his career.
But he has struggled to hold down a place in Wenger's first XI since joining from Borussia Monchengladbach - starting 10 games in all competitions to date.
Despite that, the Switzerland international insists it is normal to need time to get used to a new league and new surroundings.
"Well, actually, it's normal when you come to a new club and country," he said.
"You need to get used to the language, the philosophy of the team, the squad, the coach.
"But I do feel very happy and comfortable here, and I know the potential I have
In football you just have to develop yourself."
Wenger, whose side are set to finish second in Group A and open themselves up to a round of 16 tie against one of Europe's elite outfits, said Xhaka is now ready to make an impact in north London.
"He is adjusting," Wenger said of a player he splashed in excess of £30million on in the summer.
"Coming to a new club, where there is a big competition for places..
he has kept his focus and has done his job well every day.
"I believe he has adjusted to the intensity of the game already and the duels in the middle of the park.
"He has the stature to deal with that
He can bring a good balance between offensive efficiency and defensively as well
He has improved already all round."
Victory of any scale over Xhaka's former club at their St
Jakob-Park home will not be enough for Arsenal to leapfrog Paris St Germain at the head of the group so long as the Ligue 1 champions see off Ludogorets in France.
Ahead of the final matchday, that list of group winners who look set to be potential opponents for Arsenal is currently made up by Napoli, Barcelona, Atletico Madrid, Monaco, Borussia Dortmund and Juventus.
Although, with Sevilla, Porto, Real Madrid, Bayer Leverkusen, Bayern Munich and Napoli the potential opposition if they do top the group, Wenger does not feel there is much difference in the final positions.
"If you look at the teams, not really, no," he said if finishing second was an issue.
"We'll see what happens tomorrow with the final results
It looks quite even if you finish first or second.
"The advantage of finishing first is you play the second leg at home, and possibly 30 minutes of extra-time at home.
"We'll see
PSG are favourites to beat Ludogorets at home and win the group, but we can assess that scoreline at half-time and see where we go."
Source : PA
Source: PA