The Gers trail their Old Firm rivals by five points but have two games in hand over the Hoops, who face Inverness Caledonian Thistle in the Scottish Cup this weekend.
Rangers have triumphed in the two previous league meetings between the sides as well as knocking the Rugby Park side out the League Cup.
However Kilmarnock have won back-to-back games in the league, including last week's victory away to Hearts, which has moved them closer to the Jambos in third spot.
Walter Smith's side have struggled with injury worries in recent weeks with the manager only able to name six substitutes on the bench for last weekend's game against St Mirren as eight first-team players were ruled out.
Vladimir Weiss and Kyle Lafferty returned for the goalless draw against PSV Eindhoven in their Europa League last 16 tie on Thursday while Steven Naismith, Jamie Ness and Nikica Jelavic may be available to face Mixu Paatenlainen's side on Sunday.
One player who is likely to feature is captain David Weir. The 40-year-old has only missed one game in a season where he has made 40 appearances in domestic and European competition.
The central defender is out of contract with the Ibrox club in the summer but the former Everton player says he hasn't ruled out another season in Glasgow as long as he can retain his form.
"Obviously I wouldn't like to get to the position where I'm embarrassing myself - some might think I'm already doing that - but I'm enjoying it," Weir said.
"I want to stay involved in football. I love football and football's been good to me so I want to stay involved but who knows in what capacity or at what level.
"People have been saying since I was 32, 'this could be your last' or every bad game could be your last, but I don't think about it like that. I love what I'm doing, I enjoy what I'm doing.
"I just try and enjoy every day and try and do the best I can for myself and for Rangers."
Rangers eye chance to cut gap to Celtic
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