Defeat would see them overtaken by their opponents, with many already seeing the battle to finish best of the rest behind the Old Firm as a two-way fight.
But Hibs midfielder Rankin insists Hearts, who are nine points adrift of their arch-rivals, and Aberdeen, who are a further three points back, are still in the hunt.
"I think Aberdeen and Hearts are going to hit a run," said the 26-year-old.
"Dundee United have obviously put a run together, as have ourselves.
"I don't think it's just a two-horse race; I think there are four teams challenging for it.
"We're sitting in third at the moment and we're looking to maintain that position."
Rankin is confident Hibs have enough to keep their rivals at bay in the SPL run-in.
"If we can play to our ability until the end of the season, we'll win 90% of games anyway," he said.
"But we know it's not as easy as that.
"All the fixtures are piling up and this is when injuries and suspensions kick in.
"If we can come out of the next few months and still be in third spot, we'll be delighted."
Hibs have stuttered in the SPL in recent weeks, losing 4-1 to Rangers and drawing the Edinburgh derby.
The blip has coincided with the big freeze, which has meant the club had been unable to train outside for almost a month until they pitched up at Easter Road yesterday.
"We're not going to make that an excuse," Rankin said.
"We've had two not great results.
"But it's had an effect on everybody.
"We've been lucky enough to have an indoor area of our own."
Yet, Rankin reckons the uneven pitches at this time of year are not conducive to Hibs' style of play.
"We do suffer; we are a footballing team, there's no hiding from that," he said.
"But over 38 games, it's not all about playing football, it's about finding the battling edge as well."
That is exactly what Saturday's opponents have managed to do in the last two games after briefly nose-diving following Craig Levein's departure for the Scotland job last month.
Rankin said: "When they lost Craig Levein, at the start they struggled to be honest.
"They had a few dodgy results but I think they've got back on track since then.
"It's going to be difficult going to Tannadice.
"They've not got a manager and they're trying to impress.
"They're only two points behind and they can see that third place."
Rankin will be hoping to break a goal drought that dates back nine months, with competition in the Hibs midfield having increased since the summer arrivals of Liam Miller, Kevin McBride and Patrick Cregg.
"Personally, I feel I could add more goals - I could score a goal!" he said.
"There's only really two midfield positions available and we're battling it out.
"You've got to be on top of your game to keep your position in the team."
Dundee Utd 11/8, Hibernian 15/8, Draw 12/5