Zola has won just twice since replacing Gary Rowett in December, suffering 13 defeats in 22 games along the way.
Rowett’s Derby County became the latest club to score a victory over Birmingham, with Tom Ince’s stoppage time strike earning a 2-1 win at St Andrew’s.
The defeat left Zola’s side in 18th place, six points above the relegation zone with five games remaining this season.
The club’s board reiterated their support for Zola in a ‘vote of confidence’ on Monday, stating: “Birmingham City would like to clarify the situation in regard to Gianfranco Zola after recent articles in the media over the weekend: the club has not lined up any manager to replace Gianfranco, who has the continual full support of the Blues’ board of directors.
“Whilst we understand the frustrations caused by the run of results, the way the supporters got behind Gianfranco and the team on Saturday at St Andrew's was typical of Blues fans' passion, care for the club and desire for success, which is what we all share and much appreciate.
“The board and all departments at the club are keeping united and standing alongside Gianfranco, his staff and the players, to try and play the kind of football every Blues supporter deserves to watch.”
A descent into the third-tier of English football remains unlikely but Birmingham must turn around a run of seven winless games in order to secure their Championship status sooner rather than later.
Zola’s next game in charge sees his side face basement club Rotherham United, already relegated, at the New York Stadium on Friday.