The Germany international has entered the final year of his current contract at the Emirates.
The Nigeria international scored his first of the season in Sunday's win over Brighton.
Gunners move up to fifth as a goal in each half seals straightforward win on Arsene Wenger's 21st anniversary.
Wilshere is in the final year of his current Arsenal contract.
Giroud scored his 100th goal for Arsenal against Borisov.
Wilshere has already made two starts this season.
The Gunners will also be without Francis Coquelin for the game.
Spain boss has left both out of of his 25-man squad for upcoming games against Albania and Israel.
CEO pledges that Gunners will continue plan to reinvest all available revenue in the club's playing resources.
Arsenal beat BATE Borisov 4-2 in the Europa League on Thursday (28 September).
Ancelotti was sacked after Bayern fell to a 3-0 defeat against Paris Saint-Germain in the Champions League.
Ozil is in the final nine months of his contract at Arsenal and is yet to agree an extension.
England international produces inspired display as Gunners beat BATE Borisov.
Arsene Wenger's side make it two wins from two after 4-2 win in Belarus.
Costa Rica international out of action since suffering a knee injury on international duty on 12 July.
Sanchez, Ozil, Ramsey and Koscielny among players rested for Belarus trip.
Striker will miss games against Arsenal, Everton and West Ham United.
Israeli forward facing potential three-match ban after alleged stamp on Newcastle defender DeAndre Yedlin.
Six Arsenal U23 regulars were left out of the reserves squad for their Monday night encounter against Everton.
Manager adamant that winger will remain at the Etihad Stadium despite interest from Arsenal.
The French boss addressed the media following a 2-0 victory over West Brom.
West Brom lose for the seventh time in a row at the Emirates Stadium despite positive first-half display.