The 24-year-old has scored six goals and assisted another two for Blackburn this season - his first ever above the third tier.
Speaking via the Lancashire Telegraph, the Blackburn chief executive, Steve Waggott, confirmed: "We had a few offers for Dacky which were well chronicled and we have to keep our best players and build around them.
"It shows we respect the efforts they have put in for the club, keep them highly motivated and lock them in.
"I’ve been at clubs where every year you can have more than half of the squad turning over and it’s a big ask starting from scratch and the manager has to impose his DNA on the group.
"We’re trying to rebuild the club to help us progress and with a stable platform of players."
West Brom aren't short of options in Dack's position, having added Wes Hoolahan last month.
Although that could change if Harvey Barnes is recalled by Leicester City in January, as recent reports suggest.
For how long can Blackburn resist offers for the rumoured West Brom target?
Have something to tell us about this article?