Lord Bruce-Lockhart (Con) has been dismayed that Sir Michael Lyons, the man charting the future of local government function and finance, has recently suggested councils do not need widespread new powers.
He told a Conservative conference fringe meeting: 'I've been a little confused by what Michael Lyons has been saying in recent weeks.
'He's a friend of local government but there seems to be a slight backing away from that strong devolution of powers.
Lord Bruce-Lockhart went on to express bafflement that Sir Michael has recently appeared to rule out the relocalisation of the business rate, partially as a result of schools cash now bypassing councils - a move which effectively means councils have to raise a bigger proportion of their money themselves.
'We all knew about the direct schools grant last November,' he said. 'There's nothing new about that.'
Sir Michael will submit his report to the Treasury at the start of December but it is not yet known when, or indeed if, it will be made public.
The LGA chairman has also warned the forthcoming local government white paper could potentially be derailed by the uncertainty created by the Labour party's power struggle.