The Wearside club remains in relegation trouble in the Championship and is up for sale as American owner Ellis Short looks to cut ties.
Paul Heckinbottom of Barnsley is another name being considered as the club hunt for a replacement for Simon Grayson, who latest just a few months after the departure of David Moyes in the summer.
While Coleman is not expected to be interested in the role and is holding out for an opportunity with greater prospects, Heckingbottom refused to rule his name out of the race to take over at the Stadium of Light when recently asked about the vacancy.
"As it stands there is nothing in it," Heckingbottom told BBC Radio Sheffield.
"In the time I've been here there have been opportunities to go and if I didn't want to be here then I wouldn't be here."