Neil Lennon, whose Celtic team last week lost at Inverness to concede the title initiative to their Old Firm rivals, said following his side's 2-0 win at Kilmarnock on Sunday that he was looking for "someone to compete" with Rangers.
And Houston is adamant three points is his aim, saying: "At this stage of the season we have to win if we want to try and get third place. We'll go to Ibrox going to try to win the match - we always try and win every game we play in and Tuesday's will be no different."
Prior to the Rugby Park match, Lennon labelled United striker David Goodwillie's comments that he hoped Rangers win the SPL title and Celtic the Scottish Cup - in order for the fourth-placed side to be guaranteed a European spot - as "ill-timed".
But United beat Rangers 3-2 on their last trip to Ibrox, with Goodwillie scoring the winner, and require maximum points to overhaul Hearts in the race for third place.
For United to claim third, they must win both their remaining games and hope Hearts lose theirs - home to Celtic on Wednesday and on Sunday's final day of the season at Tannadice.
Houston added: "It's still a long shot but we'll still try for it.
"We'll try our best to win on Tuesday night and it will be up to Wednesday night's game to see if it goes to a last-day finale. I would like that opportunity."
Hearts currently hold a five-point advantage over United, who have already secured fourth place, and Houston knows if Celtic lose at Tynecastle on Wednesday, the capital club will take third.
"It's not in our hands," he added. "We could win at Ibrox and Celtic could lose at Hearts. It could go all sorts of ways, so I'm not thinking about our chances of getting third. What I'm more delighted about is the fact we've consolidated fourth."
Source: PA
Source: PA