The city council is assessing two bids to build and operate the facility in the Cross Green area but Liberal Democrats say the decision on a preferred contractor has been moved forward to the summer.
They claim the council has not made clear the reason for the delay, whether the plans have changed, nor whether the change in time scales has cost money.
Council leader Keith Wakefield proposed a referendum on the waste Private Finance Initiative project in 2008 but the Liberal Democrats have complained that there has been no announcement whether this will take place.
Liberal Democrat Councillor Ralph Pryke said: “People in Burmantofts and Richmond Hill have a right to know what council plans are for an incinerator in the area.
“The decision has been delayed by quite some time yet we’ve not heard a peep about why this is, let alone any consultation with local people. If the plans have changed, they need to explain to residents what they are doing, as this is an issue that causes serious concern in the area.
“Right now we have an information vacuum which is being filled with misinformation and half truths as the council isn’t making it clear soon what it is doing.
Fellow Liberal Democrat Coun Steve Smith said the lack of clarity was causing residents concern.
Labour councillor Tom Murray, executive member for environmental services, said: “The waste PFI project is a multi-million pound legacy that we inherited from the former Conservative-Liberal Democrat administration. This is a project that both Councillor Pryke and Smith serially voted for.
“This year alone, as the new administration, we have had to identify savings of £90m as a result of unprecedented cuts by the national Tory-Lib Dem coalition. It is worth recognising that to stop the PFI project, that the former joint local administration committed us to, would cost the council upwards of around £150m.
“It is therefore absolutely right and responsible that we take our time to explore all options available to us in order to ensure that we come back with the right decision for the Leeds. In the meantime we continue to talk to all those concerned, including local people. ”