Kiyan is the son of former Iran national youth team player and East Bengal legend Jamshid Nassiri.
In 2019, he joined Mohun Bagan to play for their U-19 side in the Zee Bangla Football League and was sent on trial for the senior team.
Ahead of the team's inter-zonal semifinal match against Uzbek side FC Nasaf in the 2021 AFC Cup, Kiyan was called up in twenty-two member squad.
[11] He scored a hat-trick for Mohun Bagan in their 3–1 derby win against East Bengal on 29 January 2022,[12] and became the youngest ever player in the Indian Super League to do so.
As 2022–23 season began, Nassiri appeared with the club on 20 August against Rajasthan United at the 131st edition of Durand Cup, in which he scored the opener but lost the match by 3–2.