The 20-year-old scored his first international goal for Denmark against the Czech Republic last Friday and reports have claimed that Arsenal, Stoke City and Tottenham Hotspur all had scouts at the World Cup qualifier.
Speculation in Denmark suggests scouts from England were again in attendance on Tuesday night when Cornelius started the 1-1 draw at home with Bulgaria.
Copenhagen have recently insisted they do not want to sell Cornelius and are determined to keep their squad intact ahead of next season's UEFA Champions League.
Cornelius' representative Jonathan Walker, however, has suggested that Copenhagen's resolve could be tested over the coming months.
Walker told Sporten.dk: "Cornelius is a hot name in England.
"I know that some Premier League clubs are considering an offer for him."