Dyche has led Burnley to the sixth spot in the table.
The German international has started only once in all competitions since Arsenal's defeat to Liverpool in August.
The Nigeria international scored his first of the season in Sunday's win over Brighton.
Wilshere is in the final year of his current Arsenal contract.
Wilshere has already made two starts this season.
The Gunners will also be without Francis Coquelin for the game.
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).
Ozil is in the final nine months of his contract at Arsenal and is yet to agree an extension.
Sanchez, Ozil, Ramsey and Koscielny among players rested for Belarus trip.
Six Arsenal U23 regulars were left out of the reserves squad for their Monday night encounter against Everton.
Ozil, 28, is out of contract at the end of the season.
Iwobi has made 64 appearances for Arsenal since breaking through during the 2015/16 campaign.
Gibbs joined West Brom in the final days of the transfer window after spending 13 years with the Gunners.
Both Mesut Ozil and Alexis Sanchez are in the final year of their contracts.
Barry, 36, joined West Brom from Everton this summer.
The Chile international has started just one league match after coming close to leaving the Gunners.
Both Walcott and Calum Chambers were forced off in the 1-0 win over Doncaster.
Sanchez and Wilshere played the full 90 minutes against Doncaster on Wednesday (20 September).
Walcott and Chambers both had to be taken off against Doncaster Rovers.
Wilshere is set to make his first start for Arsenal in over a year.
Mertesacker will lead the Arsenal academy from the 2018/19 campaign.