He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
Kohli reached the 11,000 mark in 222 innings -- beating the previous record held by compatriot Sachin Tendulkar who took 276 innings to rack up that total.
The Indian skipper was 71 not out when rain stopped play at Old Trafford in the 47th over with India 305-4.
Tendulkar still holds the record for the most career ODI runs with 18,426.