The forward returned to Tannadice on a six-month loan deal from Blackburn in the summer, with his signing seen as a coup for the Tayside club.
McInnes knows Goodwillie will be one to watch when the sides meet at Pittodrie on Saturday but he is keen to focus on what his own players have to offer.
He said: "I think the signing that really galvanised United was the signing of Goodwillie.
"For me, that shows the ambition still with Dundee United to compete.
"I know they lost Johnny Russell and Jon Daly but the re-signing of Goodwillie, and what it took to get him, suggests they've still got a lot of ambition this season.
"They are a good side. There are a lot of players there getting to know each other and they'll improve as they go along.
"For us, it's about concentrating on ourselves.
"We look at the threat of United of course, like every opponent, but we concentrate on ourselves."
McInnes hopes Barry Robson can make his long-awaited return from injury when his former club come calling.
The midfielder has been sidelined since the opening day of the season - a 2-1 win over Kilmarnock - with a knee problem which required surgery.
He returned to training this week and McInnes has refused to rule out the possibility of Robson making his comeback this weekend.
He said: "It's early days. We've still got a couple of training sessions to get through before Saturday's game and we will see how he is.
"Certainly, since the start of the week, it's been very encouraging.
"You can't ignore a player of his experience and his quality in any game, never mind such a good game as the United game."