Essien is informing Real Madrid's scouting department about the player's progress, according to Danish outlet Tipsbladet.
Yirenkyi, who scored from the bench in Ghana's 3-1 friendly victory over Scotland on Monday in Fort Lauderdale, has attracted attention from several Premier League clubs in addition to Real Madrid. The starting price for any deal is understood to be around €20m.
Essien, who played for Real Madrid on loan from Chelsea in 2012-13, remains connected to Spanish football and has been described as a trusted source for the club's assessment of African talent.
Nordsjælland have an established reputation for producing young African players through their FC Nordsjælland Right to Dream Academy model — a pipeline that has previously delivered players including Kamaldeen Sulemana to European clubs.
Yirenkyi's World Cup exposure with Ghana — who face England, Brazil and Morocco in their group — will provide the most significant audition of his career so far, and interest is likely to sharpen if he impresses across the tournament.