The SPL champions-elect may not have any money to spend in the transfer window due to their financial predicament but boss Walter Smith says he is still actively watching players he would normally be interested in signing - and the Terrors pair come into that category.
The Rangers boss said: "We do still watch transfer targets. Our scouting budget was cut quite dramatically but you do keep looking.
"The difficulty is you do not know what market you are working in. I retain an interest and we have been active in that department.
"We put the knowledge together hoping that, one day, it will be useful. It is hard because we don't know what level we might be able to bring someone in from.
Goodwillie was recently named SPL Young Player of the Year and has scored 12 goals for United this term, while fellow midfielder Conway has also had an impressive campaign, scoring four times.