The 17-year-old has made seven appearances for the Bairns this season and it had been suggested several English clubs were also interested.
"Trust me, it's 100% speculation and it gathers arms and legs," said Houston.
"If any of our players were subject to a bid from a team - if it was a good bid - the directors will take it. Simple as that."
Sunderland manager David Moyes was in the stand watching Falkirk's 2-1 win at St Mirren but did not confirm if he was there to watch the teenage left-back.
The youngster was dropped to the bench for that victory after playing six consecutive games in the first team.
"He's 17 years of age, and one of the things as a manager that you need to know is when to put a player so young and so good as Tony into the team," said Houston.
"Luke Leahy played exceptionally well for 18 months and Tony had to bide his time. Tony might have been able to go in a bit earlier if Luke had been injured.
"[Recently] I felt Luke had just slightly dipped and we had a discussion about it and it was time to put Tony in there.
"But there's also a time to know when to take the pressure off a young lad. He went into a side over the last seven games when we have been inconsistent.
"Tony was exceptional in the period he was in the team but it's the right time just to bring him back out and take the pressure off him with all the media speculation and hype that's going on about him.
"He'll get back in there again and when he does he needs to make sure he's bigger, stronger and better for it."
Several other players like Scott Arfield, Stephen Kingsley and Jay Fulton have left Falkirk and gone on to experience English Premier League football.
Houston stressed the importance of knowing when is the right time to let that happen.
"Thankfully Tony's parents are sensible," he said.
"He could have signed for a lot of big clubs when he was 13 but he chose Falkirk because he thinks the best development pathway to play football is through Falkirk.
"If he's good enough he'll get picked up by these other teams again."
Falkirk manager Peter Houston has played down newspaper reports that Barcelona are pursuing Tony Gallacher.