Bowyer was a fan favorite at St Andrew’s when he played there between 2009 and 2011, helping them in their memorable League Cup final victory over Arsenal.
The 43-year-old would be interested in talking to his former club, if the opportunity arises, because of instability at The Valley.
Charlton was bought out by Paul Elliott last week – their third owner this year – and sit two points from safety in the relegation places in the Championship.
Ex-Burton Albion manager Nigel Clough is also on Birmingham’s shortlist to replace Pep Clotet, who will leave his head coach role at the end of the current season.
