The 19 year old turned down the proposal and Houston has now claimed Allan's representatives demanded the player be made one of the club's highest earners, despite the fact that he has played just 242 minutes for the first team.
Houston has been infuriated by the situation and is particularly critical of the player's agent, John Viola.
"Scott has rejected our offer and I'm very disappointed," Houston said in the Daily Record.
"He was offered the best deal this club has ever offered to a teenager but doesn't want it.
"When it comes down to a 19-year-old demanding to be the third-highest paid player at the club after two-and-a-half games then I wouldn't pay him it even if I could afford it.
"That's what his agent asked for at first. He wanted wages in line with guys who have been playing at this level for years - I think he's being wrongly advised.
"That tells me where the priorities lie. I can't be bothered with people who are only motivated by money. We won't give Scott any more money because he has still to prove himself. He has had two good games, that's it. He might get a big club but will he play?
"For me he should be looking to play 50-100 games here and then perhaps move to a bigger club.
"But he and his advisers want to do it their way so whatever happens will be up to them."
Agent Viola later hit back and defended his client against accusations that he is only interested in money.
He said: "Scott is not greedy, all he wants is to play. It's the club's prerogative to play him during contract talks."