BNP Chairperson Khaleda Zia's doctors said she can be taken abroad once she becomes consistently stable.
With oxygen support, her oxygen saturation level remains 100 percent and she needs one litre of oxygen an hour, said a doctor involved with Khaleda's treatment.
The doctor, who is in a 10-member medical board, said the former prime minister's oxygen level fluctuates without oxygen support, but the dependency has decreased.
"We advised the family members to take madam [Khaleda] abroad once she gains more stability," he told The Daily Star yesterday.
Her blood pressure was 120/80 at 5:00 pm yesterday when her respiratory rate was 15-20 per minute.
Doctors said the improvement should continue in order for her to be able to fly.
Family sources said Khaleda's aide Fatema, her brother Shamim Iskandar and his wife will accompany her if the government clears the hurdles to her flight abroad.
She will be taken either to London, the UAE, Singapore or Thailand.
"Once we get the passport, we will apply for a UK visa. We may also seek visas for Singapore and Thailand," said a top BNP leader.
BNP sources said Khaleda's family members received "a positive signal" from the UK government regarding her treatment in a London hospital.
BNP leaders said getting the government approval remained the main challenge as she was released from jail through an executive order of the government on the condition that she does not leave the country.
That is why Khaleda's brother Shamim Iskandar wrote to the home ministry seeking approval on Wednesday night.
The BNP chairperson can be flown abroad if the law ministry amends the order, BNP sources added.
Khaleda did a medical checkup in Singapore before her imprisonment, and if the government of the city-state allows, she might be flown there.
If they fail to take her to Singapore, her family members will consider taking her to Thailand.
Khaleda's younger son Arafat Rahman Koko's in-laws live in Thailand, and when Koko was released from jail after the army-backed caretaker government assumed office in 2007, Koko went to Thailand and stayed there for five years.
Khaleda's family members are also considering taking her to the UAE and get her treated there for a few days before leaving for London. That travel time can be divided that way.
"The family prefers London because her son Tarique Rahman has been living there since September 2008. But everything depends on the government's approval and her physical condition," said a party source.
Khaleda was admitted to Evercare Hospital on April 27, three days after she tested positive for coronavirus for a second time. She first tested positive on April 11. She also has arthritis, diabetes and eye problems.
She was taken to the hospital's Coronary Care Unit with breathing difficulties Monday afternoon.
The government released Khaleda from jail on March 25 last year, suspending her sentence as per section 401 (1) of the Criminal Code of Procedure. The suspension was later extended twice.
The BNP chairperson landed in jail on February 8, 2018, after a special court sentenced her to five years in prison in the Zia Orphanage Trust corruption case. On October 30, 2018, the High Court raised her punishment to 10 years.