The "Moaviya group", a militant organisation plans to mount a suicide attack on Sheikhupura district jail, where 45-year-old Asia is being held, The Express Tribune quoted its sources as saying. An intelligence report issued last week has corroborated threat to her life.
Punjab police and jail authorities subsequently beefed up security due to the intelligence report and the assassination of Taseer.
Asia Bibi was sentenced to death last year after being convicted under the blasphemy law for insulting Prophet Mohammed. She denied the charge and said she was framed by a group of Muslim women with whom she had a row.
Taseer, who backed a call for Asia Bibi to be pardoned, was gunned down in Islamabad on Tuesday by a police guard who said he was angered by the Governor`s criticism of the blasphemy law.
According to official figures, 131 people are being held in jails across Punjab on blasphemy charges.
Eleven of them have been sentenced to death, including Asia Bibi, who was the first woman to be given the penalty.
Though no one has been executed after being convicted under the controversial law, 35 people, including Taseer, who were accused of committing blasphemy or defending those charged with blasphemy have been killed between 1990 and 2011.
They were either victims of extra-judicial killings or found dead in prison in suspicious circumstances.