Dack, 24, scored 18 times in League One for Blackburn last term and has continued that impressive form into the new season, netting four times in four appearances in all competitions.
Leicester City have recently been credited with an interest in the midfielder, and it has been reported that the Foxes are lining up a January swoop.
However, according to The Sun, West Brom are also firmly in the race, with the Baggies still hopeful of securing a loan deal for Dack despite seeing a £7m bid rejected.
The report claims that West Brom want to sign Dack on an initial loan before completing a permanent deal when the transfer window reopens at the start of 2019.
Blackburn are said to value Dack - a £750,000 arrival from Gillingham in June 2017 - in the region of £10m.