At least 18 people have died throughout the UK in open water in recent weeks during the hot weather.
Smith put forward the motion at a full council meeting during Drowning Prevention Week, an annual campaign run by Royal Life Saving Society UK to raise awareness about water safety.
Councillor Kalvin Neal supported the proposal but noted the location of the former lido is occupied.
“Although it is something that could be looked at, potentially that isn’t the best place, it could be somewhere else that might be better,” he said.
Currently, the city’s only council-run lido is at Albert Avenue Pools and Fitness, which opened in 2023 after a £10.5m makeover.
According to the Local Democracy Reporting Service, the motion also called on the council to carry out a comprehensive promotional campaign on safe water-play practices and facilities.
Smith also asked the council to look at how all primary school children in Hull could get free weekly access to the city’s leisure centres in the school holidays for swimming lessons.
When researching, she said she found statistics showed children from less advantaged families were significantly less able to swim than their peers.
“I don’t think that’s acceptable. Swimming is not a luxury, it’s not an optional extra, it’s a key life skill,” Smith said.
She added if the motion “prevents even one family from that unimaginable grief of losing their child”, it would have been worth it.
A cross-party working group will explore Smith’s proposals.
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