The ex-Leeds United boss has been out of work since leaving the Elland Road club in the summer after just four months in charge.
Heckingbottom has held talks with Hibs to succeed Neil Lennon in charge of the SPL club, and is 8/15 favourite for the job.
Michael Appleton is another leading candidate, but reports in Edinburgh suggest that talks have broken down and Hibs are now closing in on Heckingbottom.
The 41-year-old was in the frame to succeed Simon Grayson as Sunderland manager last season, having impressed at Barnsley, only for Chris Coleman to get the job.
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Heckingbottom was then named Leeds boss but was in charge for just 16 games before being replaced by Marcelo Bielsa in the summer.
Heckingbottom failed to play a first team game for Sunderland, before signing for Darlington.
Ex-Newcastle and Sunderland midfielder Lee Clark has also been linked with the Hibs post.