Shahbaz Taseer, 27, was kidnapped yesterday by four armed men near his office in Gulberg area.
Assistant Superintendent of Police Fazal Hamid, who is part of the investigation team, told PTI today that they had been working on different leads including that of the involvement of the ''Mumtaz Qadri Lovers'' group as also a property dispute angle.
The Taseer family had been receiving threats since the killing of the former governor in January this year at the hands of his own security guard, Mumtaz Qadri, of the Elite Force who was opposed to Taseer's opinion that the country's blasphemy laws needed to be amended.
Confessing to his crime, Qadri had said he had killed Taseer for "committing blasphemy".
The anti-terrorism court hearing the case, adjourned the proceedings today till September 10.
Taseer had requested President Asif Ali Zardari to suspend the death sentence of a Christian woman, Asia Bibi, in a blasphemy case.
Religious extremist groups, who said Qadri had done a "commendable job to kill a blasphemer," had warned the court and the government against convicting him.
Punjab Governor Sardar Latif Khosa has accused Shahbaz Sharif's Punjab government of "having indirect link with the kidnapping of Taseer junior".