Betis have identified the 22-year-old as one of several targets as they plan for next season, according to Estadio Deportivo, with the club working on multiple positions they feel need strengthening.
The rejected Saudi bid, though not aimed at Betis themselves, sends a clear signal to the Seville club that a significant investment will be required if they want to prise Dju away from Denmark.
Dju, whose full name is Franculino Gluda Dju, enjoyed a breakout campaign in the Danish Superliga, finishing as the division's top scorer despite having much of the second half of his season disrupted by injury.
His performances have attracted interest well beyond Betis, with Premier League clubs including Everton, Fulham and West Ham United monitoring his situation, along with Atletico Madrid, Bayern Munich and Galatasaray. Midtjylland are understood to value the forward at around €45m, more than double the figure suggested by some market valuation sites, and have shown no willingness to let him leave for the Saudi offer already turned down.
Raised in Portugal after being born in Bissau, Dju came through Benfica's academy before joining Midtjylland in 2023, where he has developed into one of the most sought-after young forwards in European football.
Real Betis, who have been searching for reinforcements up front after a lack of goals hampered them in recent transfer windows, will need to decide whether they are willing to compete financially with wealthier suitors or look elsewhere for their attacking reinforcement this summer.
Physical fragility has been flagged by some as a risk factor in any potential deal, with Dju having already dealt with a serious injury lay-off during his prolific campaign in Denmark.
That concern is understood to be something Betis's sporting department are weighing carefully before committing significant funds to the operation, given the fee now being discussed would represent one of the largest outlays in the club's history.
Should Midtjylland hold firm on their valuation, Dju would become the most expensive sale in Danish football history if a fee close to the figures being discussed is eventually agreed with any suitor.