Wolfsberger, meanwhile, have slipped to third place in Group K after successive defeats to Dinamo Zagreb.
CSKA Moscow have found points much tougher to come by in Europe this season, having drawn three of their Group K matches.
The 0-0 draw with Feyenoord in their last match was the fifth draw in their last seven games in the Europa League since the start of last season – no team have been involved in more stalemates in the competition.
They do however sit joint-top of the Russian Premier League – with 32 points after 10 league wins from 16 matches – although they suffered a 1-0 defeat to Rubin Kazan on Sunday.
CSKA Moscow won their only previous home game against Austrian opposition back in 1981, beating Sturm Graz 2-1 in a UEFA Cup match.
Victory for Viktor Goncharenko's side would be their first in this season's competition and could move them into second place if Feyenoord lose to Dinamo Zagreb.
Wolfsberger are competing in only their second Europa League competition after qualifying for the group stages for the first time in their history last season.
The Austrian side have however suffered successive defeats to Dinamo Zagreb this campaign, which has seen the Croatian side move above them in Group K.
Thursday night will be Wolfsberger's first away game against Russian opponents, with their only previous match against a Russian side coming in the reverse fixture in October, which finished a 1-1 draw.
Ferdinand Feldhofer's side have only won one of their last nine games in the Europa League, with that lone victory coming away from home against Feyenoord.
Wolfsberger could better their points tally from last season's Europa League, with a win against Moscow moving them onto seven points and with a good chance of qualifying for the knockout stages for the first time.
CSKA Moscow Europa League form: DDLD
CSKA Moscow form (all competitions): WLWDDL
Wolfsberger Europa League form: DWLL
Wolfsberger form (all competitions): WWLWLD
Striker Fyodor Chalov, who has yet to score in the Europa League this campaign, is set to lead the line for the Russians once again.
Wolfsberger midfielder Matthaus Taferner is back from suspension, having been sent off against Dinamo Zagreb at the start of November.
CSKA Moscow possible starting lineup:
Akinfeev; Fernandes, Diveev, Magnusson, Zaynutdinov; Maradishvilli, Oblyakov; Sigurdsson, Vlasic, Kuchaev; Chalov
Wolfsberger possible starting lineup:
Kuttin; Novak, Baumgartner, Lochoshvili, Scherzer; Stratznig, Wernitznig, Liendl, Peretz; Dieng, Joveljic
We say: CSKA Moscow 1-1 Wolfsberger
Both sides need a result if they are to have a chance of qualifying for the knockout stages. With both sides lacking consistency and little between the two teams, Thursday night could see another score draw.