The ePetition on Peterborough City Council's website warns that closing the popular family site would "leave children without a safe place to play."
The cash-strapped council is currently proposing to stop operating the water park as it would save Â£18,000 a year, but critics say this is small change compared to a Â£24 million deficit it is trying to tackle.
In a sign that the cut might be overturned the deputy leader of the council, Cllr Wayne Fitzgerald, tweeted that he had requested that the cabinet "do all it can to continue the funding for Bretton Water Park."
He added: "I for one will not be supporting this proposed cut. We need to find a way to keep it open/alternative funding sources. E.G. The Parish Council in Bretton could help?"
Cabinet adviser Cllr Steve Allen also tweeted: "Fully support another look at how to maintain this excellent community facility. Suggested at Cabinet we look at sponsors and also believe it's important we encourage real engagement from the the Parish Council."
The city council is hoping Bretton Parish Council will take over the running of the water park, but the parish council has already set its budget for next year.
The ePetition, under the headline 'Save Bretton Water Park', states: "Bretton Water Park is a hugely popular site that many families use. It is free, safe and clean which makes it a huge asset to the area and it is beneficial to a wide range of age groups.
"Families from the whole of Peterborough (and beyond) use this park and to close it would leave children without a safe place to play."
If the ePetition, which has been signed by 23 people, reaches 500 signatures it will trigger a debate at the next Full Council meeting.
The consultation on the council's budget proposals, which includes the Â£18,000 saving from not maintaining the water park, continues until March 5.
Full Council will then vote on the proposals two days later.