The Hammers tried to sign the 21-year-old at the start of the season, but will doubtless have to front an even bigger bid after the player's heroics against Manchester United
The 21-year-old, who scored the Danish side's first goal in a 2-1 Europa League win over Manchester United on Thursday, is highly rated in his home country, and was called up to the national team at just 20 years old.
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And Bilic has revealed the Hammers tried to sign the starlet as a long-term investment.
"He's young, he's 21 so we wanted to get him for the future," Bilic told ITV.
"We watched him against Southampton and in a few other games. He's got pace, he's brave, he's young and he changes direction well.
"He's a great prospect. We wanted him, but we must give credit to him and the people around him - they decided that it'd be better to stay in Denmark for another year."
Manchester United will endeavour to turn around their 2-1 deficit when they host Midtjylland at Old Trafford next Thursday.