Officers were called to the reserve at 8.21pm on Sunday 30 May, and attended along with the ambulance service and fire service, who got two-year-old Greyson Birch out of the water.
Greyson was subsequently taken to Southampton General Hospital where he sadly died on Thursday 3 June.
Our enquiries have identified that earlier in the day on Sunday 30 May, Greyson also visited Lakeside Country Park in Eastleigh between 6.45pm and 7.15pm.
We are issuing a photo of Greyson taken that day so you can see the clothing he was wearing – a blue striped top, dark shorts, and white trainers. He may have had a small push along bike with him at Lakeside.
Detective Inspector Matt Gillooly, who is leading the investigation, said: “Our investigation is tracing all of the steps leading up to Greyson’s tragic death, and we are looking at places he may have visited prior to Swanwick Lakes.
“We want to know if anyone at Lakeside Country Park saw him that afternoon and anyone he was with. Please contact us if you did, as any detail around Greyson’s movements that day, no matter how insignificant it may seem to you, could prove crucial in determining the full picture of this case.
“Were you there that afternoon? Do you recognise Greyson or his clothing from the photos we have released? Please contact us if you do.”
An 18-year-old man from Southampton who was previously arrested in connection with this incident on suspicion of neglect remains on bail until 30 August.
Anyone with information is asked to contact police on 101, quoting 44210210811.
Alternatively, you can contact the independent charity Crimestoppers 100% anonymously on 0800 555 111, or via their anonymous online form at https://orlo.uk/A7y8G