Wilshere, who spent last season on loan at Bournemouth, is expected to be handed a lifeline and start for the Gunners as Arsene Wenger rotates his squad.
When asked about the 25-year-old, Wenger said: 'He continues with the spirit and focus. There was always pressure to come back as quickly as possible and expect a lot. He can keep calm, focus on his job and he is on a good way in training.
'He is getting stronger and stronger every day. He was injured and a bit behind the other players but he is getting better and better.'
Europa League glory would guarantee a Champions League place next term, but Wenger believes the easiest way to qualify is via the Premier League.
'We don't calculate that this is a way to qualify for the Champions League,' Wenger said at a Wednesday press conference ahead of Cologne.
'It is not the best chance but one of the opportunities. I came out many times saying the best way to do it is the top four of the Premier League.'
Olivier Giroud, Theo Walcott, David Ospina and Alexis Sanchez are all expected to be drafted in for the match against the German side, while the French manager confirmed both Mesut Ozil and Aaron Ramsey will be 'rested completely'.
Arsenal face Chelsea in the Premier League at Stamford Bridge on Sunday afternoon, meaning a number of key players could sit out the Group H opener.
Alexandre Lacazette, Danny Welbeck, Granit Xhaka, Laurent Koscielny and Petr Cech all missed Wednesday morning's training, all but confirming they will watch from the sidelines.
Wenger believes the Thursday to Sunday fixtures will not hinder his team's progress this season, despite having a notable impact on teams in previous campaigns. He said: "When you play Wednesday-Saturday it's similar to Thursday-Sunday.
"We played Wednesday night in Barcelona and Saturday morning at Everton [in March 2016] and we won. You have to not get caught in your mind with preconceived ideas. In three days you can recover."