The 29-year-old paceman was suspended from all forms of cricket on Sunday as police investigate allegations he "tortured and abused" the maid who is undergoing treatment in hospital.
A police officer investigating the case said Hossain's mobile phone is now being tracked and officers are hopeful of arresting him soon.
"We've mobilised ten mobile teams (of officers) to arrest him. We're making raids almost everyday and are now tracking mobile phones," inspector Shafiqur Rahman told AFP.
The Bangladesh Cricket Board (BCB) suspended Hossain from all forms of cricket until the case is resolved, effectively ruling him out of next month's two home Tests against Australia.
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Hossain, who played 38 Tests and 51 one-day internationals for Bangladesh, missed the recent series against India and South Africa after twisting his ankle in a Test match in May.
Hossain and his wife Nritto Shahadat have been on the run since police raided their house on the night of September 6 after officers found the injured and crying maid on a street in Dhaka.
"She told us that the couple beat her very often. Her hand was charred with a hot cooking paddle. She had injury marks all over her body," Rahman has said.
A team of doctors is treating the girl at the Dhaka Medical College Hospital.