The Millers are on the lookout for a new manager following Steve Evans' surprise departure on Monday and are in the process of drawing up a shortlist.
Hasselbaink, who has guided Burton to the top of League One in their first ever campaign at that level, appears to have caught their eye, but has turned down the chance to leave the Pirelli Stadium.
Brewers chairman Ben Robinson told the Burton Mail: " Burton Albion were asked permission to speak to the manager by another club
"We thank them for informing us of their interest in our manager.
"I discussed the approach with Jimmy, and his response was to say that he was very flattered and grateful for the opportunity but feels that this would not be the right option for him at this time.
"But we thank the club for their interest and for their professional approach."
The 43-year-old former Holland international is fast gaining an impressive reputation in his first job in English football, having overseen seven wins from the opening 10 games of the season on the back of winning promotion from League Two last season
Rotherham, who lost their first game since Evans' departure on Friday night against Burnley, are under the caretaker charge of Eric Black, who has hinted he will not apply for the job
However, Neil Redfearn, Stuart Gray and Nigel Clough are all expected to be interviewed over the weekend.
Source : PA
Source: PA