Aston Villa are also understood to be interested in Dack, who is keen on a move to the Premier League.
Both sides have been promoted from the Championship and are preparing for life back in the top flight of English football. Brighton and Hove Albion are also keeping tabs.
West Bromwich Albion, meanwhile, are also thought to still be keen after having a deadline day bid for Dack rejected last summer.
The 25-year-old has enjoyed two hugely impressive seasons at Ewood Park since joining from Gillingham. In 2017/18 Dack scored 18 goals and provided eight assists as Blackburn finished second in League One.
The forward immediately took to life in the Championship as well, netting 18 times in all competitions last term. Rovers were expected to offer Dack – whose current contract expires in 2021 – a new deal as a reward for his performances.
However, that has not been forthcoming, prompting Premier League sides to step up their interest.
Why Sheffield United could win race for Bradley Dack
West Brom are likely to be the outsiders for Dack as they cannot offer him top tier football for 2019/20.
There could also be question marks over how serious Villa will be in their pursuit. After all, they have already signed someone in Dack’s position this summer when they secured Jota from Birmingham City.
Brighton could pose a problem for the Blades, though. Their new manager Graham Potter is aware of the Blackburn star’s talent from his time in charge at Swansea City.
Yet for the South Yorkshire club, Dack could be exactly what they need. The Sheffield Star reports that a new attacking midfielder is one of Chris Wilder’s priorities in the transfer market this window.