Heckingbottom is regarded as one of the favourites by most bookmakers but while he has acknowledged that discussions have been held with the Tykes hierarchy, the former defender has insisted that there have been no developments with a club who he represented during his playing career.
The 40-year-old is quoted by the Yorkshire Post as saying: "No, there hasn't. We have been sat here before, so the situation is no different. I have been asked these sorts of questions before about different clubs at different times. It is just what happens in football, it is all hypothetical.
"Until anything happens, I can't tell you because I don't know the club's thoughts on it or my thoughts on it. We've obviously spoken and had these conversations (him and Barnsley) but they will remain private."
Heckingbottom has won 36 of his 89 games in charge of Barnsley since first taking over in February 2016.