The Scotland Under-21 forward is in the form of his life and his goals have been an integral part of United's solid start to the Clydesdale Bank Premier League season.
Goodwillie will lead the line against Neil Lennon's men on Sunday, and he said: "Am I in the best form of my life? Certainly as a professional I am, but when I was in boys' football I used to score about eight in every game. Joking aside, yes this is probably the best I've felt about the way I'm playing and I'm scoring goals just now so hopefully that continues."
He added: "On Sunday I'd settle for just the one if it means we win the game.
"It is going to be hard to continue our current run of form with Celtic coming to Tannadice but I'm sure they're thinking the same.
"They have been in fantastic form, winning all their games and Neil Lennon has them flying.
"When he was given the job some people said he'd struggle but he's proving them wrong.
"I'm not surprised because he's been there for years. He knows the club inside out and will have the respect of the players.
"They've signed a lot of new players so there is a step into the unknown for us but it's the same for them as well."