SNP councillors want to bring forward the project to replace the Allander Leisure Centre by four years earlier than planned.
Under the current plans building work is not due to start on the project until 2022 - following several delays.
The need for a new leisure centre was identified as far back as 2007 and the SNP group say they are growing increasingly frustrated by the delay in delivering the project for the community.
Ian Mackay, SNP group leader, said: “Firstly I’d like to bust the myth that the council needs to wait until the developer CALA Homes has released funds for this project.
“The council is not reliant on the capital from the housing being built - these funds will just go into a big pot and they will not be ring fenced or allocated to this project.
“It is being delayed because the council is running an austerity budget.
“We think they should borrow money just now while it’s at its cheapest level ever.
“Investment is desperately needed just now to promote economic development in our area and create jobs.
“The council hasn’t even started designing it yet or scoped it to decide what facilities it will include.”
The SNP Group would like to bring the start of work forward to 2018/19 instead of 2022/23.
They believe this could reduce the cost of the project, including saving £5 million on design and construction. They say the income from the leisure centre could also be increased by at least £2 million.
Council Leader Rhondda Geekie, said: “Significant developer contributions associated with the development of the
Kilmardinny masterplan area have been secured towards the delivery of a new Allander Leisure Centre.
“The council is legally obliged through planning agreements to use this funding only for this purpose.
“We have the same ambitions as Cllr Mackay as regards the Allander project.
“The Allander Champions Group will meet again shortly and we are happy to look at the timescale of the capital programme in relation to the project.
“There has been an unprecedented level of capital investment committed towards new facilities across East Dunbartonshire - despite severe financial pressures which are ongoing.
“Approximately £45 million is due to be invested in the Bearsden and Milngavie area - including the proposed new Allander centre, Bearsden Hub, future Milngavie Hub, new primary school and Kilmardinny House.
“The phasing of the Allander was reaffirmed by Council as part of its 10-year capital programme earlier this year and was not challenged by any party during the budget process.”