Goodwillie, who made his Scotland debut against the Faroe Islands in November, has attracted reported interest from clubs including Rangers and Blackpool after scoring 11 times this season.
Unless players depart - and Goodwillie appears the most likely player to be leaving Tannadice - Houston will not be recruiting this month as he is without the funds to do so.
It is a situation he is more than comfortable with.
The United boss 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."