Zia, 80, who is the leader of the Bangladesh Nationalist Party, was admitted to a private hospital on November 23 with a severe chest infection affecting her heart and lungs, doctors and senior party officials said.
Her party has regained prominence after Sheikh Hasina, Bangladesh's long-serving former prime minister, was ousted in a student-led uprising last year.
Rahman, who has lived in London since 2008, wrote on Facebook on Saturday that his return to Bangladesh was "not entirely" in his control, fuelling speculation over political or legal hurdles.
The interim government led by Nobel laureate Muhammad Yunus later said it had "no restrictions or objections" to his return.
"There are no obstacles in this matter," Yunus' press secretary Shafiqul Alam said in a Facebook post.
The interim government will issue a travel pass within a day if Rahman wishes to return to Bangladesh, de facto foreign minister Touhid Hossain said on Sunday.
Rahman has been acquitted in all the cases against him since Hasina's ouster in August last year, effectively removing the legal barriers that once complicated his return.
The BNP, which boycotted disputed elections in 2014 and 2024, has gained momentum since last August and is seen as a frontrunner in Bangladesh's shifting political landscape.
