Saif-ul-Malook said he had already spoken with Dutch politicians and ministers, although he was yet to make an official asylum request.
Pakistani Christian woman Asia Bibi's lawyer on Friday said he was seeking asylum for his client and her family in The Netherlands amid violent protests in Pakistan by radical Islamists against her acquittal in a blasphemy case.
Saif-ul-Malook said he had already spoken with Dutch politicians and ministers, although he was yet to make an official asylum request, reports Efe news.
Speaking at a vigil for Asia Bibi organised in Vianen near Utrecht by the foundation Persecuted Christians, which covered the costs of her nine-year long legal battle in Pakistan, the lawyer said he would file a written request with the appropriate authorities in the next few days.
A Dutch Foreign Ministry source said only affected persons can file asylum applications and no third parties were allowed to do so on their behalf.
Last week, a majority of parties in the Dutch Parliament urged the government to temporarily take charge of Ms Bibi and her family after she was acquitted by Pakistan's Supreme Court of blasphemy charges for which she had been sentenced to death eight years ago.
Since her acquittal and release, she has been threatened amid widespread protests that accelerated her departure from a Lahore prison and her transfer to Islamabad on Wednesday.
Malook said Ms Bibi, her husband and children were under the protection of the Army and police in the wake of threats from radical Islamists who demanded a public execution, rejecting her acquittal.
The lawyer was also forced to flee to The Netherlands last week but has not filed an asylum application to stay permanently in the country.
On Thursday, the Dutch Foreign Ministry made an official offer to him to join a special programme for human rights activists under pressure in their home countries.