Mrs May has previously called for the death penalty to be abolished globally when asked about Ms Bibi’s case.
Ms Bibi was arrested in 2009, accused of insulting Islam’s prophet during an argument with fellow farm workers and sentenced to death for blasphemy.
Lawyers have denied she ever insulted Islam.
Campaigners have long-criticised Pakistan’s blasphemy laws, saying they are misused to abuse religious minorities.
Pakistan’s Supreme Court acquitted Ms Bibi on Wednesday, upholding the law but saying there was not enough evidence to convict her.
Ms Bibi’s lawyer fled Pakistan on Saturday while fearing for his life, according to reports.
Nasir Saeed, the director of CLAAS UK – a charity that supports persecuted Christians in Pakistan, called for Mrs May to intervene quickly.
“The lives of Asia Bibi and her family are in danger as long as she remains in Pakistan, as the protests following the verdict have shown,” he added.