The Sun reports that the Ravens have opened direct discussions with the former England international, who is available after his spell in charge of Italian side Cesena. Bromley parted company with Andy Woodman last week, bringing an end to a five-and-a-half-year tenure that included two promotions and the FA Trophy.
Cole, 45, made his first move into senior management with Cesena in Serie B during the closing stages of last season. He oversaw eight matches before leaving, and is now being linked with a return to English football in a first-team role.
Bromley have struggled in their first League One campaign. They have won only two of their opening 11 league fixtures and were sitting 22nd in the table at the time of the report. Interim manager Byron Webster has taken charge while the club consider their options.
Blackburn Rovers assistant manager Mike Dodds is also reported to be on the shortlist, although Cole is described by The Sun as the leading target. Any appointment would follow a remarkable rise under Woodman, who guided Bromley from non-league football into the EFL and then to the third tier.
Woodman’s departure came despite that progress. In a statement quoted by The Sun, he said:
“It is with great disappointment that my time at Bromley Football Club has come to an end after five and a half years of continued success and achievement.
“When I arrived at the club, we had a vision of where we wanted to take Bromley Football Club.
“To have taken this club from non-league football to League One in just five seasons, as well as winning the FA Trophy at Wembley against a fantastic Wrexham side, is something I will always be incredibly proud of.”
Cole’s coaching experience includes work with England, Chelsea, Everton and Birmingham City. As a player, he won major honours with Chelsea and Arsenal and earned 107 caps for England.
He has previously outlined the kind of football he wants his teams to play, saying:
“I played as a defender all my life, but I do not want to coach defensive football.
“My idea is to entertain the fans, focus on possession, fast attacks and winning games.”
Bromley’s interest remains at the discussion stage, with no appointment confirmed.