The 20-year-old, who is top scorer in the Danish league with 17 goals, has attracted the attention of a number of clubs across Europe this season.
However, the Daily Mail believes that the Premier League duo will make their interest concrete in the summer.
Potters boss Tony Pulis confirmed that he had travelled to watch the youngster in action against OB Odense last week, but refused to state whether he will be making an offer.
"We have targets and we're keeping tabs all season on them," said the Welshman. "He was mentioned, but whether we do any business is another thing.
"I don't know about signing him, but while I was there I caught a cold with the snow blowing in on me."
Cornelius has scored one goal in four appearances for Denmark.