District Coordination Officer Noorul Ameen Mengal has made the job offer to Shabana Naz on behalf of Chief Minister Shahbaz Sharif during his meeting with the bereaved family on Monday. City Police Officer Afzaal Ahmed Kausar was also there.
A Rs500,000 cheque has also been given to the woman by Punjab government.
Irshad Ahmed killed his three minor daughters -- six-year-old twins Iman and Fiza and seven-year-old Chishman -- at Chak 113-JB, Phulahi, Jhumra, and escaped.
Meanwhile, Chak Jhumra police also registered a triple-murder case against Ahmed on the complaint of Abdul Sattar, brother of Ms Naz.
The applicant stated in the FIR that Ahmed used to quarrel with his sister over giving birth to girls.
Police said raids were being conducted to arrest the suspect.