The 31-year-old defender was one of the Clarets' standout players in the Premier League, playing in every league game and showing off his leadership qualities and regimented defensive style.
He will be a key player as Sean Dyche looks to win promotion back to the Premier League at the first attempt, but his talent has impressed Derby boss Paul Clement, who wants to bring him to the iPro Stadium.
He would be a key player in the Rams’ set-up as well, and the Midlands club have seen a £1.5 million bid rejected for his services already.
However, this has not put them off, and as they prepare to further strengthen following the arrivals of Darren Bent and Scott Carson, Clement is willing to raise his bid.
There is no reference in the report to how high Derby are willing to go, but for a 31-year-old it is likely that the £1.5 million offer was close to their maximum valuation.
Should Derby manage to clinch a deal for Shackell, they would be signing a proven Championship level defender to partner alongside Alex Pearce, who will arrive at the club on a free transfer when his Reading contract expires.