Walter Smith's side can make it two league championships in a row with a win in the Capital, although anything less than a Celtic win against Dundee United at Tannadice in Sunday's early kick-off, would settle matters even before a ball is kicked in Leith.
Nish was part of the Kilmarnock side that lost 2-1 to Celtic in April 2007, a result which handed the SPL title to the Parkhead side, and knows the misery of having to watch someone else pop the champagne corks.
Nish had bagged a first-half leveller that day after Jan Vennegoor of Hesselink had opened the scoring for the Hoops but trudged off the Rugby Park pitch dejected after Shunsuke Nakamura hit a stoppage-time winner to claim the title with four matches remaining.
That goal sparked wild celebrations among the away support and their players and Nish admitted: "You never like to think that someone is coming to your ground to win the league, the last thing you want is to see them celebrating with the trophy at the end of the game. Obviously, we will be doing our best to try to spoil the party, we don't want them parading the trophy in front of their fans.
"I wasn't here the last time Rangers won the title at Easter Road but the same thing happened to me at Kilmarnock and I remember how that felt.
"Celtic came to Rugby Park needing a result to win them the title and, unfortunately for me, they got it with a really late goal.
"It's a horrible feeling and not something I want to have to go through again and I'm sure the boys who were here the last time will feel the same."
While much of the focus this week has been on Rangers' title prospects, Nish and Co still lead the race for fourth place in the SPL and a spot in the Europa League qualifiers next season.
With Motherwell and Hearts keeping up the pressure from fifth and sixth spot, Nish knows there's no room for error in a season that started so promisingly.
He added: "Our main focus is Hibs and, although there has been a lot of attention on Rangers and the title, this is a massive game for us in terms of winning a place in the Europa League.
"We want three points to help make sure we get fourth place. That's what we're aiming for now and we want to give ourselves the best shot at it that we can.
"There are no friendlies in this league at the best of times but especially now because every point counts for us.
"We've got some really big games coming up in the next few weeks, against teams who will also be looking at that fourth place but we'll be focusing 100 per cent on Rangers this weekend and only when that one is out of the way can we start to look ahead at the rest of the games that are left.
"I think the manager has helped to lift the mood among the guys lately and it's been down to some hard work in training and on the park.
"I think we played quite well against Celtic and managed to score a couple of goals.
"Unfortunately, we lost three goals at the end of the day so it wasn't enough, but I think we played better than we have done in recent weeks and hopefully we can improve on that again this weekend when we play Rangers."
Nish was delighted for fellow hitman Anthony Stokes after the Irishman picked up the Clydesdale Bank Goal of the Season award this week for his stunning strike against Rangers at Ibrox back in October. However, he thought that is team-mate had been unfortunate to miss out on the gong for Young Player of the Season and continued: "We've not heard too much from him so far – which is unusual for him!
"It was a great goal that he scored at Ibrox and probably deserved to win it.
"To be honest though, I was quite surprised that he didn't win the award for Young Player of the Season as well because he's done well and scored a lot of important goals.
"He scores like that in training all the time, all he does is practice his shooting I think.
"He's got great ability and I think he proved that with the goal at Ibrox.
"I thought he had a chance but, at the same time, you can't really argue with David Goodwillie either, because he's had a great season as well."