LGC understands Ms Miller - currently Bradford’s deputy chief executive - was selected from a shortlist of three women earlier this month.
She has not yet been formally appointed as she is still negotiating terms and conditions with the association.
John Ransford, the current deputy chief executive who is filling in for the suspended Paul Coen, is due to retire in the spring.
However, if appointed, it is understood Ms Miller intends not to take up her position on a full-time basis until late next summer.
The role of deputy chief executive also encompasses the position of director for local government services.
As part of the association’s business development strategy, the Improvement & Development Agency, Local Government Employers, 4ps, the Leadership Centre for Local Government and the Local Authority Coordinators of Regulatory Services are being brought together into one ‘local government services company’.
The advertisement for the job said the association was seeking “one of the most able chief executives or an exceptional
deputy chief executive/strategic director” for the post which pays an “attractive six figure sum”.
The LGA said it could not confirm if an appointment had been made or if there was a preferred candidate.