The 51-year-old is in charge following Craig Levein's departure to become Scotland manager and could be offered the post permanently if he shows up well over the next few weeks.
United are believed to have him as their preferred candidate but Houston has refused to tout himself for the position.
His only focus is on the job in hand and he senses his team are ready to pull off a shock result in Glasgow on Wednesday night.
He said: "I went to the Rangers game on Sunday and was impressed by them.
"They are full of confidence and are scoring goals for fun. But that doesn't frighten us.
"There is a lot more to come from our boys. We've dipped a bit in the last few weeks and I don't think we've been at our best.
"We struggled a bit against St Mirren before getting the goal to win the game.
"Against Hearts, if we were anywhere near our best we would have won that match and then everyone knows what happened when Rangers came to Tannadice.
"Rangers were very good that night but, having looked back at the video, we were nowhere near what we can be.
"So the challenge for the players is to recapture the level of performance we showed earlier in the season.
"Last weekend, we created a lot of chances without scoring to win the game and on another day we would have got the full points.
"But that's gone now and you can only influence the future.
"I have to say, I felt a wee spark come back to the training on Monday.
"We had to train indoors but the lads were really buzzing and I can sense a feeling among them that they want to make up for the defeat against Rangers earlier in the month.
"Having Morgaro Gomis back will help because he's a big player for us.
"If we play to our capabilities then I'm sure we will give Rangers a decent game."
United are without Andy Webster under the terms of his loan from Rangers, but Gomis returns after serving a ban against Kilmarnock last weekend.
Darren Dods will come into the side for Webster, while youngster Craig Hill was flown in from Northern Ireland to sit on the bench.
Houston revealed: "Andy Webster is not available because it's Rangers and Scott Robertson is missing.
"But we knew Webby wouldn't be there so big Darren Dods will come back into the team.
"I've also recalled Craig Hill, who is a young centre-half, from his Christmas holiday to come and sit on the bench."
Rangers v Dundee Utd. Click here to bet.