Yes, but not often, only less than 5% of the time. Why?
The meniscus is divided up into three zones. Two of the three zones have a very poor blood supply. Blood is needed to aid in a repair. Sutures can be placed to hold the torn meniscus together, but if there is no blood supply the meniscus will not heal.
Most meniscus tears occur in the area where there is poor blood supply. Therefore repairing the meniscus is not an option, only removing the torn portion is the treatment. The majority of people when they have their knee scoped are NOT getting a meniscal repair they are undergoing a partial menisectomy.
Those that can get their meniscal tear repaired usually have tears that occur at the same time an ACL injury occurs. The meniscal tear pattern in that injury tends to occur in the region of the meniscus that has a good blood supply.
This image with red circle reveals a tear in the red zone of the meniscus.
The blue arrow in this image indicates the white zone, while the red arrow points to the red zone.
The blue arrow in this next image shows the white zone of the meniscus while the red arrow indicates the red zone.
This shows an ACL tear.