Officers want to speak to anyone who witnessed the incidents.
Three fires in Nuneaton are being treated as linked by Warwickshire Police.
Investigating officers are now appealing for witnesses to the suspected arson incidents.
Police were called to the Vale View Recreation grass area on Haunchwood Road shortly before 4pm on Thursday (11 August) after a report of a fire.
Shortly afterwards, around 4.15pm, officers were contacted by the fire service about a fire that had taken place in the field on Montana Walk.
Officers were also called by a member of the public who reported the bushes and river edge of Sandon Park Recreation Ground on Shawe Avenue had been burnt.
It is believed that the fires may have been started deliberately.
Warwickshire Police want to speak to anyone who witnessed the incidents or who saw people acting suspiciously in the areas at the time.
Anyone with information should report it online or call 101 quoting the following incident numbers:
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251 of 11 August (Haunchwood Road incident)
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264 of 11 August (Montana Walk incident)
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23/34438/22 (Shawe Avenue incident)
Alternatively details can be provided to the independent charity Crimestoppers anonymously on 0800 555 111.
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