The former England Under-21 midfielder was left out the side's 1-0 Premier League victory over Mark Hughes' men on Wednesday, with speculation mounting over a possible switch to the Britannia Stadium.
But Oatway refuted those suggestions and said Cattermole's absence was merely due to a knock.
"There's nothing [in that]," he said. "There's been one article, but no business I know of whatsoever.
"He just had a little bit of a knock, he's been training with it, he's trying to carry on training with it.
"But if flared up a bit yesterday and again today. It's a long season and we need everybody. If we played him today and we lose him for three or four weeks we could shoot ourselves in the foot."
Sunderland moved out of the Premier League relegation zone for the first time since August thanks to Adam Johnson's tap-in, with Steven N'Zonzi sent of for the visitors in the second half.
England international Johnson has now either scored or assisted in Sunderland's last seven Premier League goals, and Oatway was thrilled with his contribution in a tight encounter.
He added: "Nobody is under any illusions about his [Johnson's] ability. We have him firing on all cylinders. We needed a bright spark.
"At this moment in time we put cotton wool around him, he's played with a little knock but he's got another goal and that's fantastic for him and us.
"You're under no illusions as to what Stoke are about, they'll put balls in the box and fight tooth and nail for every ball. There will be times you have your back against the wall. You have to fight and we did that."