Scottish Cup holders United's inability to score in their 0-0 draw with Ross County - a re-run of last season's Hampden final - demonstrated what life could be like without Goodwillie, but Houston has insisted club chairman Stephen Thompson has not been contacted about the 21-year-old, who has netted 11 goals this season.
Houston said: "The chairman has been keeping me well informed if anything's happening and nothing's happening."
Goodwillie, who made his Scotland debut against the Faroe Islands in November, will be available for United's Clydesdale Bank Premier League clash with Motherwell at Tannadice on Wednesday night after serving a suspension in Saturday's draw with Ross County.
The United boss expects a quiet transfer window as he is without funds to strengthen his squad.
Houston will only be recruiting if players depart, but he would rather retain his current squad.
He said: "If somebody goes, I know a couple of people I'd like to get in, but I'll not get anybody in unless we get people out.
"As yet, there's nobody out and hopefully it stays that way.
"If we keep the same squad between now and the end of the season and get some of the ones fit who are first-team players, then I'll be more than happy."