The local authority is in consultation with staff and unions over 37 senior management posts – including strategic directors and assistant directors.
Matt Burghardt, Bradford Council's assistant director, human resources, said: "As part of the chief executive's proposals to rationalise the council's senior management structure and to comply with legal requirements, a Statutory Section 188 Notice is being issued notifying the trade unions of proposals to restructure the council's senior management.
"A full consultation is ongoing with trade unions and the staff affected. The section 188 notice formalises a minimum 30-day consultation process with all those affected by the proposals."
The council remained tight-lipped over the actual proposals and was unable to say how much money they could save.
A report published last month revealed the cost of Government cuts to Bradford Council this year are more than 30m.
A financial position statement gave some indication of the scale of the savings and cuts necessary before April, said Bradford Labour group.
At the time Bradford Council leader, Ian Greenwood, said: "These coalition cuts are unprecedented, draconian and punitive. They will threaten services, public and private sector jobs, undermine the local economy, and will hit people on low and moderate incomes hardest."
He warned that there would be "much worse to come" when the Chancellor publishes the comprehensive spending review in October.