Norway's Protector Forsikring is the insurance provider for the building's owner, the Royal Borough of Kensington and Chelsea.
"Gross claims all products preliminary estimated to GBP 50 million," it said as it released its second-quarter earnings.
"Figures are preliminary, uncertain and will include both property, liability and other potential related costs," it added.
The figures were preliminary and uncertain so they could change, Protector said.
The company had previously said the fire would cost property insurers more than 25 million pounds ($32.4 million), with 20 million covering the building itself and the rest going to additional expenses such as alternative housing.
Protector had also said the cost would largely be covered by its reinsurance program through Germany's Munich Re.
Britain's Jardine Lloyd Thompson was the insurance broker for Grenfell Tower.