Rangers v Hibs: Giovanni Van Bronckhorst sends Hibs warning and explains Aaron Ramsay's match fitness
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The Light Blues' chastening 3-0 defeat by Celtic at Parkhead last Wednesday night saw the Hoops take a one-point lead over their Old Firm rivals at the top of the cinch Premiership.
"I mentioned after the game, we showed the way we can play and that is our standard," said the Dutchman, who will be without midfielder Ryan Jack who picked up an ankle knock against the Jambos while defender Filip Helander could be ready for his comeback next weekend.
"That's the level you want to reach every game.
"Not only playing-wise tactically, but also character-wise and this is definitely the way to go forward and to make sure tomorrow we keep the levels high and make sure we have the same performance.
"We were very dominating and that's also good to see and the case is now to go on this path and make sure we keep the levels and also be sharp and also be able to confront when players aren't doing it or making mistakes, just make sure you keep the levels of the team as well."
Jack's start against Hearts was the first in a year after recovering from a knee injury but Van Bronckhorst confirmed the injury was not too serious.
He said: "Ryan Jack is out because he has a problem with his ankle. He will not be in the squad or playing tomorrow.
"He had an injury, a knock on his ankle during the game which gave him a lot of discomfort so hopefully, we can make him ready in the coming days to train again.
"It's not a serious injury but the game tomorrow is too soon.
"With a tight schedule and so many games in a week, sometimes the game just comes too quick."
Aaron Ramsey, the deadline-day loan signing from Juventus, came on as a second-half substitute against Hearts but Van Bronckhorst stated that the Wales international midfielder is not fit enough to start against Hibs.
He said: "No, I don't think he's ready to start yet.
"Aaron is improving each day and I think it's good to see the difference he's already made in a week, he will become better and better but starting a game for him is too soon.
"But he will be closer to starting a game the more minutes he plays and the more sessions he has with the team."
Van Bronckhorst left Helander out of Rangers' Europa League squad and he will miss the knockout tie with Borussia Dortmund but revealed the Sweden defender is almost fit again after being out since last September with a knee injury and could be in contention for the Scottish Cup tie against Annan on Saturday.
"It was a hard decision to leave him out of the European squad because we only had 23 players we could put on the list," said Van Bronckhorst.
"So at that time I chose the players who are fit to play games and also players who can play in different roles.
"Filip is really close to starting to get minutes again, hopefully, we can involve him at the weekend so he starts playing and also be involved with the squad in the league and the cup competition but the only competition he cannot play is in Europe.
"Once he will make his minutes he will be back in the squad, it's looking quite positive for him so he will be back playing really soon."