After last year's Scottish Premiership champions thrashed Ross County, they saw off the challenge of Astra Giurgiu in the Europa League on Thursday to give themselves a good chance of qualification from the group stages.
Victory on Sunday afternoon would also see them overtake their opponents in the standings while still having a game in hand on the top three.
Deila could revert to the team that eased past Ross County, meaning that Stefan Scepovic could miss out despite netting his first goal for the club against Astra.
Kilmarnock made a mixed start to the season but three successive wins have put them into the mix in the standings, with a win at Celtic Park potentially moving them joint-top.
Killie haven't lost since falling to defeat at Inverness Caledonian Thistle at the end of August and Allan Johnston will have belief that his team can pull off a shock away from home.
Possible starting lineups
Celtic: Gordon; Izaguirre, Mulgrew, Lustig, Van Dijk; Denayer, Brown, McGregor, Stokes; Johansen, Guidetti
Kilmarnock: Brennan; Connolly, Barbour, Pascali, Chantler; Hamill, Clingan, McKenzie, Johnston; Obadeyi, Magennis
Sports Mole says: 2-0