According to the security officials, Mullah Salam was initially injured during clashes with the Afghan forces and succumbed to his injuries after he was taken to the hospital Chardara district.
The Taliban militants group has not commented regarding the report so far.
The Taliban militants launched a coordinated attack on the strategic Kunduz city earlier this week with an aim to capture the control of the city but the Afghan forces managed to repulse the attack although sporadic clashes still continue in the outskirts of the city.
The Taliban militants have launched numerous attacks on Kunduz city since it was retaken by the Afghan Special Operations Forces earlier in the month of October.
The Taliban insurgents were accused of horrific criminal activities after they seized control of the city, including target killings, rape, kidnappings, use of civilians as shields, looting of public and private properties.
The Independent Human Rights Commission of Afghanistan said at least 50 civilians were killed and over 350 others were wounded.
However, the rights organization said the number could be relatively higher as AIHRC said their statistics was based on hospital reports and several others had not been taken to hospital after they were killed or injured.