The Potters sacked ex-Black Cats boss Alex Neil earlier this week following a woeful run of form that saw them lose four of their last five Championship games.
Stoke are sitting 19th in the Championship standings on 22 points, just three points ahead of teams in the relegation zone.
Stoke are now on the lookout for a new manager and have already drawn up a shortlist of candidates they are looking into.
It has been claimed that Mowbray, another former Sunderland manager, is on the radar.
The 60-year-old was sacked by Sunderland recently in a move which was greeted with surprise given his achievements during his time at the club.
Mowbray got Sunderland into the playoffs last season and many were left shocked by his sacking at the Stadium of Light.
Former Birmingham City manager John Eustace and ex-Fulham boss Slavisa Jokanovic are also on Stoke’s radar.
If Mowbray takes over as Stoke boss then he will come up against Sunderland in the Championship next month.
