PDP president Mehbooba Mufti wants a passport issued to Geelani but the BJP is bitterly opposed.
Mehbooba Mufti told reporters on Wednesday that she would see to it that Geelani gets the passport as it was a humanitarian issue.
But she added that the final call would be taken by the home ministry.
Senior PDP leader and MP Tariq Hameed Karra has also come out in support of a passport to Geelani.
The BJP said a passport can be given to Geelani only if he accepts the accession of the state to India and affirms that he owes allegiance to the constitution of the country.
"How can you apply for an Indian passport unless you accept that you are an Indian citizen and owe allegiance to the constitution of India?" BJP spokesman Khalid Jehangir told the media.
Geelani had been issued a restricted passport for a duration of one year in 2007, 2008 and 2011 but he did not visit Saudi Arabia then.
On Tuesday, Geelani's wife and son visited the regional passport office here. Sources in Geelani's separatist outfit said he could not complete the formalities as he was under house arrest.
Director General of Police K. Rajendra Kumar has, however, denied that Geelani was under house arrest.
Mehbooba Mufti also said that other separatist leaders including Mirwaiz Umer Farooq, Shabir Shah and Muhammad Yasin Malik hold Indian passports and that two of them have been visiting abroad.