The town's three community recycling centres (CRCs) are located in Stockton Heath, on Sandy Lane, Gatewarth, on Barnard Street, and Woolston, on New Cut Lane.
The village site was saved in 2014 following a huge public outcry over plans to shut it.
A petition opposing any proposed closure was launched in April after the Warrington Guardian revealed the tip had been earmarked for closure.
The petition, which has secured more than 3,000 signatures, has been submitted to the authority.
During Tuesday's executive board meeting, members approved plans to carry out a six-week consultation 'on the current and potential future provision of waste recycling services' at the facility.
In her report to members, Cllr Judith Guthrie, executive board member for environment and public protection, said: "Given the current site constraints of Stockton Heath, with particular regard to the size and access restrictions, together with the impact on immediate neighbours, officers understand that obtaining the required environmental permit would be challenging, in respect to both achieving technical and environmental specification compliance.
"However, before any decision is made on the future of Stockton Heath, we propose to undertake a consultation on the provision of waste recycling services at the site to obtain consultees' views on future options."
The current budget for the operation of the three CRCs is £854,854, which includes disposal and management fee haulage costs.
However, the cost of operating these sites in 2017-18 was £1,149,110 – an overspend of £294,256.
Deputy council leader Cllr Russ Bowden said: "What is clear to me is, if we are designing a waste system for Warrington with a blank sheet of paper, it would not look anything like this.
"I think what we can see is the Stockton Heath site is far more expensive to run than the other two.
"It is right the council consults with the public about the future provision of that site.