The teenager, from Birchwood in Warrington, Cheshire, was found by members of the public lying injured on a path in Linear Park, Culcheth, at around 3:13pm on Saturday.
Cheshire Police previously said there was no evidence to suggest that Brianna, who was a transgender girl, was the victim of a hate crime.
But on Tuesday, the force released a statement saying all lines of investigation were being explored, “even if it was a hate crime.”
A boy and a girl, both 15, were arrested on suspicion of Brianna’s murder and detectives were given a 30-hour extension to question the two suspects further, police said.
A GoFundMe crowdfunding page set up to help the schoolgirl’s family surpassed £70,000 in donations just one day after it was set up.
More than 4,500 people from 41 different countries have contributed to the fundraising efforts, GoFundMe confirmed.
Candlelight vigils, organized by members of the transgender community, will be held across the country in memory of the teen.
Over the next few days, vigils will be held in cities including London, Glasgow, Leeds and Belfast, with events in Liverpool and Bristol on Tuesday night.
In a tribute issued after Brianna’s death on behalf of her family, they said the teen was a “much loved daughter, granddaughter and little sister.”
The statement continued: “She was a larger-than-life character who would leave a lasting impression on everyone who met her.
“Brianna was beautiful, witty and hilarious.
“Brianna was strong, fearless and unique.
“The loss of his young life has left a huge hole in our family, and we know the teachers and their friends who were involved in his life will feel the same way.”
Several police vans were seen parked in the surrounding area after the incident, with several uniformed officers patrolling the park.
A large part of the area was cordoned off with police tape, and police dogs were also seen on the scene.
The principal of Brianna’s school, Birchwood Community High School, said they were “shocked and truly devastated” by her death.
Several schoolchildren, still in their school uniforms, laid flowers at the police cordon at the entrance to the park on Monday.