The 22-year-old has enjoyed a prolific spell in front of goal so far this campaign, netting 16 goals in 20 Championship appearances.
According to The Sun, Sevilla remain the frontrunners to land the Chile international, though both Southampton and Leeds are also closely monitoring the striker.
Even though Brereton Diaz has just over seven months remaining on his contract at Ewood Park, Blackburn value their star man at around £20m.
Southampton head coach Ralph Hasenhuttl is keen to partner Brereton Diaz with striker Adam Armstrong, who moved to St Mary's from Blackburn for around £15m in the summer, however, the Saints may need to sell first to fund his potential purchase.
Meanwhile, Sevilla – who have a history of recruiting players from England including Erik Lamela, Jesus Navas, Fernando and Suso – believe they can persuade Brereton Diaz to move to La Liga, as Julen Lopetegui's men challenge for a place in the Champions League once again this season.