It said officers were aware of social media rumours circulating and encouraged people to “stop speculating”.
The body of an 18-year-old man was pulled from the reservoir on Friday night.
The fire has sent large plumes of smoke for miles around across the wider region.
Greater Manchester Fire Rescue Service is also investigating and has warned people to be “really, really careful” of dry vegetation which can easily ignite.
“This is a live police investigation,” said Det Insp Andrew Day of GMP.
“We would encourage people stop speculating regarding this and if you do have information, please report it to ourselves.”
The force also thanked the fire service for “working tirelessly in extremely challenging conditions to contain the fire”.
Road closures remain in place at Holmfirth Road and Bank Lane with no access to Dovestone Reservoir, GMP said.
It reminded people to avoid the affected areas so to enable emergency services to carry out their work.