Liefering striker Adeyemi has scored eight goals in 13 appearances while on loan in Austrian Bundesliga 2 this season, and has also netted three times for parent club RB Salzburg in the UEFA Youth League.
It was in the Youth League that Liverpool have had first hand experience of Adeyemi.
Barca, or more specifically academy director Patrick Kluivert, have been long term admirers of Adeyemi, but according to Sport, Liverpool and Arsenal are also keeping tabs on him.
German giants Borussia Dortmund have also been linked with the teenager.
If Barca were to win the race, they plan to build up Adeyemi's experience in the Barca B side but would promise him a future of La Liga action.