Midfielder Dack, who joined Blackburn from Gillingham for £750,000 last summer, has scored 12 goals for the League One promotion contenders.
He is under contract at Ewood Park until 2020 and boss Tony Mowbray is reluctant to sell.
Blackburn will be hoping to see off the mounting interest in Dack’s signature before the transfer window slams shut.
The Sun claim Aston Villa, Leeds United and Middlesbrough are all keen.
Dack, 24, has established himself as a goal machine at League One level since making his Gillingham debut in 2012.
He was named the League One player of the season at the end of the 2015/16 campaign.
Rovers gaffer Mowbray is delighted with Dack’s contributions and, speaking last month, he said: ”I want to sign good players, and I knew I was doing that when we brought Bradley Dack into the football club.
“I wasn’t hoping for anything from Bradley apart from working really hard and being the player I know he is.
“He’s contributing to winning football matches and working so hard, which is an important thing with me for Bradley.
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“He’ll get the rewards – as we all will – if he carries this on and continues to influence games for us.
“The main attribute is that he continues to fight for the team and playing his part for the team.”
Cardiff boss Neil Warnock wants Dack to beef up his squad to sustain their promotion charge.
The Bluebirds are currently third in the Championship table and are also hunting Bournemouth striker Lewis Grabban.