Sally Cummins, 61, was left in a critical condition when a gang of three men opened fire on her Coleraine home in October.
Police do not believe she was the intended target of the gunmen, thought to belong to the North Antrim UDA.
Detectives are examining whether the incident was linked to the sudden death of na woman in the same property on the Bushmills Road in September.
It is understood officers are investigating a drugs link to the shooting.
Outlining details of the reward offered by the Crimestoppers charity, PSNI Detective Chief Inspector John Caldwell said the victim had made good progress in her recovery but remained in hospital.
The detective said two types of weapons were used – a shotgun and handgun.
He said one of those weapons had also been used in a series of other unsolved attacks in Coleraine.
“The 61-year-old is now making good progress, but remains in hospital,” he said.
I am still treating this incident as attempted murder… I hope the substantial reward leading to the arrest and conviction of those responsible for this callous shooting will encourage people to give vital information to the charity. The reward is also available to anyone
who can provide information leading to the recovery of the weapons.
Detective Chief Inspector John Caldwell
Mr Caldwell provided further details of the incident at a press conference in Belfast.
He made clear no one else was in the property when the shooting was carried out on 5 October.
The senior detective said a link to the recent sudden death in the property was “one line of enquiry”.
He said CCTV footage from the area formed part of the police investigation.
“The 61-year-old grandmother was sleeping in a chair downstairs due to her various health problems when she was shot in the head by one of the many bullets fired at her house by a gang of three men,” said Mr Caldwell.
“I believe the attack was carried out by North Antrim UDA members and two different types of weapons, a handgun and a shotgun, were used.
“These reckless and dangerous thugs do not care about who they hurt in the process of trying to exert their so-called power in this area.
“It is purely about their egos, power and what they can obtain financially.
“It beggars belief that they fired over 10 shots, smashing numerous windows in the house, not caring that this vulnerable woman was inside.”