The winger played an instrumental role in United's 4-2 victory over Kilmarnock on Saturday by setting up the first three goals before netting the fourth with a stunning strike.
Goodwillie is desperate for Conway, who is out of contract in the summer, to remain with the Tangerines.
He said: "Conway was on fire and set up three and scored one. I think it would be a massive miss for the club if he moved on.
"I don't think people realise how much he does. He creates so many goals and if he does go, hopefully we can replace him."
Source: PA
Source: PA