The youngster has been a standout performer for Ghana at the World Cup and has long been on the Seagulls' radar as a potential long-term replacement for Carlos Baleba, who is expected to leave Brighton for Old Trafford this summer.
The 20-year-old has been watched extensively by scouts from across the Premier League's elite, with Manchester United, Arsenal, Chelsea and Liverpool all said to be monitoring his progress alongside Brighton. Scouts from around a dozen clubs, Brighton included, were present to watch Yirenkyi in action against FC Midtjylland earlier this year.
Yirenkyi joined Nordsjaelland from the Right to Dream academy and signed a contract extension that ties him to the Danish club until 2030. He has continued to impress since, registering goals and assists in the Superliga while also winning senior caps for Ghana.
According to the Daily Mail, a move for the highly-rated midfielder could now be on the cards, with the report suggesting Nordsjaelland have already rejected offers in excess of £25 million this summer and are holding out for around £40m.
Nordsjaelland's willingness to dig in over their asking price reflects their ambition to smash the Danish Superliga's transfer record, which currently sits at close to £22m.
Brighton's interest is not new. The club have followed Yirenkyi's development closely since his move to Denmark and believe he could follow a similar path to Baleba, who arrived at the Amex as a raw talent before establishing himself as one of the Premier League's most sought-after midfielders.
With Baleba's departure now seen as increasingly likely, Brighton are ready to move quickly to identify his successor.
United's interest adds a further complication to Brighton's plans, with Ineos having already sent scouts to run the rule over the midfielder. Should the Red Devils firm up their interest, it would set up a fresh transfer battle between the two clubs, having already gone head-to-head for Moises Caicedo in recent years.