The Ghana international came through the same local academy as Tottenham midfielder Mohammed Kudus and his form in Denmark now has him on the shopping lists of several English clubs.
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Arsenal and Bournemouth have had scouts to check on Yirenkyi in recent games and have come away impressed.
The Sun says Brighton are also interested, with the Seagulls viewing Yirenkyi as a replacement for wantaway midfielder Carlos Baleba this summer.
Yirenkyi, 20, has a contract with FCN to 2030.