According to The Sun, Ivarsson accidentally killed himself while playing with a shotgun.
The youngster is said to have got a hold of the weapon by taking it out of a locked gun closet.
Ivarsson's father is believed to be a keen hunter, but it is not known whether his gun was involved.
Sigurdsson has yet to publicly speak on the passing of Ivarsson, the half-brother of his wife Alexandra.
The Everton midfielder, his wife and other members of their family paid tribute to the late Ivarsson in Icelandic newspaper Morgunblaðið.
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“It breaks our hearts to write these words," the family tribute read. "The first word that comes to our minds is gratitude.
"Gratitude to have been able to be with you during this short time you were here and enjoy your wonderful presence.”
Ivarsson tragically lost his life on September 8, five days before Sigurdsson played in Everton's season opener against Tottenham.
Sigurdsson joined Everton from Swansea City in the summer of 2017 for a then club-record fee of £40million.
In 115 appearances for the Toffees, Sigurdsson has scored 24 goals and provided 16 assists for the Merseysiders.
The Iceland playmaker has started on the bench in Everton's opening two games of the Premier League campaign, coming on as a substitute on both occasions.
The Toffees have enjoyed a winning start to the season, securing victories over Tottenham and West Brom to occupy top spot in the English top-flight.
Carlo Ancelotti's side will be back in action on Wednesday night, travelling to Highbury Stadium to take on League One side Fleetwood Town in the third round of the Carabao Cup.