United chairman Stephen Thompson revealed there had been two formal approaches for the in-form 21-year-old.
"Nobody has put any bids in for the player or for any of our players," Houston said.
"So until such time that there is any bids in for our players, there is no point talking about it.
"We know that if David Goodwillie moves on to something better and the club gets the money they are looking for, he will be sold.
"But at this point there is no point talking about it because there are no bids on the table."
Houston will be without Goodwillie in the short term at least with the striker suspended for the Scottish Cup fourth-round clash with Ross County, courtesy of his second booking of last season's competition in the final against the same opponents.
United could also be without Danny Swanson, who has been suffering from illness, while Craig Conway is not ready to return from knee surgery.
"Swanson has a bit of an injury so he is a wee bit of a doubt," Houston said.
"Craig Conway is back training with us but he has been out for quite a while so it is probably too early to put him back in. But he will be back in the first-team squad in the next couple of weeks."