Anthony has returned to the UK from Brazil and will face Greater Manchester Police for questioning over the abuse allegations made against him, the PA news agency said.
The 23-year-old, who joined Manchester United from Ajax last summer, has been on holiday with the Premier League club since September 10.
Anthony faces several allegations of physical aggression towards his ex-girlfriend Gabriela Cavallin, who spoke to Brazilian publication UOL earlier this month.
The winger denied these allegations, as well as further claims of assault by Raisa de Freitas and Ingrid Lana.
Anthony said in a statement on Sept. 10, “I want to maintain my innocence of the things I have been accused of and I will fully cooperate with the police to help them get to the bottom of the truth.”
The winger has been in Brazil since early September when he joined the national team but was dropped from the squad when the allegations emerged.
Anthony returned to England on Tuesday after cooperating with police inquiries in Brazil and is now set to meet with GMP. He remains on leave and is understood to be handing over his phone to police for verification.
The player was voluntarily questioned by Brazilian police in June but was not arrested or charged.