Such a suggestion founders on the issue of compensation, as Houston would be entitled to a severance package were he to be removed now, while Falkirk would also be looking for money should United appoint Steven Pressley, who is considered one of the front runners to take over.
Pressley will meet the United board this week, with Billy Dodds already having done so. However, Houston is insistent he will not be hurried out of the door, even after watching his side fail to clinch an elusive home victory, despite Gary Mackay-Steven having given them the lead against Ross County.
"I don't see any reason [to leave before his contract expires]," said Houston, whose side have not won at Tannadice for 11 matches. "I want to be here; we are not far off a European place so I don't see any rush to change it. As far as I'm concerned I'm going to be here until May."
With Aberdeen not hosting Hibernian until this afternoon, United were afforded an opportunity to move to within a point of the European places but it seemed to take time for them to warm to the task. The initial efforts were given a chilly reception by supporters at the break. Not that County had fared much better.
The home side's Gavin Gunning sent a header into the side netting after just 30 seconds, awakening the game to a sense of possibility, but it was soon allowed to doze off again. Rocco Quinn tried his luck with a low shot that spun wide but County more often tried the patience of those looking on.
Mackay-Steven had a shot blocked by Scott Boyd after 13 minutes, the chance manufactured by Stuart Armstrong, who was restored to the starting XI after being given time off following the death of his mother. He proved a composed figure if lithe figure, casually robbing Quinn of possession after 25 minutes only to be denied a return pass from Johnny Russell when he found space in the penalty area.
It seems necessary to pick out Armstrong since he would become upstaged by Mackay-Steven, as is typical of a winger whose every stepover tends to go viral on the internet. Mackay-Steven was more benign yesterday but still provided the telling moment for his side, collecting a pass from Russell after 52 minutes and arcing a shot into the top corner of the net.
His goal baited County and forced them to open up. A dominant win in their last away game – against St Mirren last weekend – will have ensured a sense of perspective despite a somewhat limited display and the draw gained at Tannadice enabled the Highland side to further extend the gap that exists between them and Dundee at the bottom of the SPL table.
The point was earned thanks to Richard Brittain, the midfielder striding forward after 82 minutes to curl a fierce shot beyond Radoslaw Cierzniak. It was Brittain's seventh goal of the season and further embellished his importance to a County side that can effectively coast to the end of the campaign.
However, it also brought into rude focus how much Brittain will be missed when he moves to St Johnstone in the summer. "He will be hard to replace but it is not until next season that we need to look at that," County manager Derek Adams said.