The newspaper reported on Thursday that Blackburn had knocked back West Brom's £7 million bid for Dack. And it claims their latest was potentially worth £15 million, with £11 million of that paid up front and the rest in add-ons.
According to the Sun, the attacking midfielder would have been open to the move, despite having only signed a new deal earlier this summer.
And the newspaper suggests Blackburn's refusal to cave could leave West Brom facing a future battle with Leicester for Dack, for whom the Foxes are 'willing to wait' for his signature.
West Brom, who sold Nacer Chadli to Monaco earlier on Friday, had until 5pm to strengthen their squad with loan - or loan-to-buy - signings, more than three weeks after the window closed for Leicester.
Dack, who cost Blackburn £750,000 upon signing from Gillingham a year ago, has scored two goals in his first three Championship appearances, with another two arriving in his one EFL Cup outing this season.
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