Rochdale have sacked manager John Coleman and his assistant Jimmy Bell.
The League Two club have begun 2013 with three straight defeats and sit 14th in the division - six points off the play-off positions.
And Rochdale confirmed the end of Coleman's 12-month reign in a statement on their website.
It read: "The regrettable decision has been made following the club's recent run of poor form. This decision was not taken lightly and was made following extensive discussions at board level.
"The club would like to thank both John and Jimmy for all their hard work and endeavours over the last 12 months and would like to wish them well for the future.
"The club hope to name their replacement before we travel to Cheltenham for our next league match on Friday evening."
United travel to face the champions on the back of a 3-2 win away to Kilmarnock last weekend, but knowing they will have to up their standards even more if they are to get a result.
And Houston, who revealed last week he'll be leaving the Tannadice helm at the end of the season, insists they have got to keep the ball against Celtic.
Houston said: "It's another big test. It will be a case of when we get the ball we have to keep it as much as possible.
"Ball retention is always important against a quality side like Celtic and it will be the same for this game.
"I'm sure that if we pass the ball like we can, we can do well.
"Kilmarnock get a lot of praise for being a passing team but I thought we did that very well against them at the weekend, and I'll be looking for my players to continue that at Celtic."
United came from behind to earn a last-gasp 2-2 draw with the Hoops on Tayside back in November.
But Houston knows they are still outsiders to pull off a shock in Glasgow, although he reckons that could work in their favour as they prepare to take on Neil Lennon's men.
He said: "There will be a different level of expectancy against Celtic compared to what we had at Kilmarnock.
"We're probably not expected to get much because of the way Celtic are playing and they're at home.
"But sometimes these games don't always go the way they're expected to and this is a challenge for our guys.
"It's up to them to go out and show what they can do and give it their best shot on the night.
"I've got belief in my players and we know what we're capable of on our day.
"We want to go there and enjoy ourselves and hopefully have something to show for our efforts."
United welcome back midfield pair Stuart Armstrong and Richie Ryan from injury, while defender Brian McLean is free from suspension.
Houston said: "It will be good to have these guys back.
"We've had a pretty young bench for the past couple of games but this will hopefully help matters.
"We don't have the biggest of squads but we just have to work with what we've got."
