Rangers, Blackpool, Swansea and Bristol City have been linked with bids for the 21-year-old striker, who could depart cash-strapped United this month if a club match the £1.5million valuation.
United were given a glimpse of the future without Goodwillie in the 0-0 draw with Ross County in the Scottish Cup last weekend, but the striker returned from suspension to score his 12th goal of the season in Wednesday night's Clydesdale Bank Premier League defeat of Motherwell.
It was the Scotland international's fourth goal in three games ahead of the clash with Hearts. United first-team coach Kirk said: "He's a big player for this club. We'd love to hold on to him.
"I think we missed him last Saturday. When you put the ball up top you know you're going to get something - he's going to get a chance or a shot away on goal."
Asked how Goodwillie, who always appears to be full of confidence, was coping with the speculation, Kirk added: "He's all right. Goodie just gets on with it - it doesn't affect him at all."