Rangers, Blackpool, Swansea and Bristol City have been linked with bids for the 21-year-old striker, who scored his 12th goal of the season in Wednesday's victory over Motherwell and could depart cash-strapped United this month if a club match the £1.5million valuation.
Asked how Goodwillie was coping with the speculation, Kirk added: "He's all right. Goodie just gets on with it - it doesn't affect him at all. 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."
United, who endured a weather-enforced five-and-a-half-week break in November and December, had not won since November 6 when they met Motherwell.
In the six games prior to the Well match, they had lost one and drawn five.
But Kirk believes United were back to their best on Wednesday.
"We were absolutely delighted the way we played," he said.
"We have been a wee bit flat, but on Wednesday night we clicked.
"From start to finish we played really well and we made plenty of chances."