Stephen Archer, 50, of Openshaw in Manchester, is a suspect in the attack at his 49-year-old sister's home that left the victim with 70% burns.
Detectives say initial investigations suggest petrol was thrown over her before she was set alight.
Petrol station staff have been urged to contact police if they see Mr Archer.
Supt Arif Nawaz, of Greater Manchester Police, said: "We are appealing to those who work in petrol stations to be extra vigilant and call police if you think you see him.
"Stephen usually wears a baseball cap and carries a large rucksack. He is known to travel on a bicycle.
"We have reason to believe Stephen could be carrying several bottles of petrol in his backpack and a man was seen fitting his description cycling away from the scene.
"We have followed several leads and have received some very helpful information but unfortunately we have still not found him."
The victim remains in a serious condition and is fighting for her life in hospital.
A police spokesman said: "She is still critically ill and our specialist support officers are supporting the family through this extremely difficult time.
"We can assure the victim, the family and the wider public that we are doing everything we can to find the person responsible and bring them to justice."
A 19-year-old woman escaped uninjured from an upstairs window of the house, with help from neighbours.
Police hunting a man suspected of setting fire to his sister have asked petrol station workers to keep a look out for him.