Provided are a computer program product, system, and method for using an attribute of a write request to determine where to cache data in a storage system having multiple caches including non-volatile storage cache in a sequential access storage device. Received modified tracks are cached in the non-volatile storage device integrated with the sequential access storage device in response to determining to cache the modified tracks. A write request having modified tracks is received. A determination is made as to whether an attribute of the received write request satisfies a condition. The received modified tracks for the write request are cached in the non-volatile storage device in response to determining that the determined attribute does not satisfy the condition. A destage request is added to a request queue for the received write request having the determined attribute not satisfying the condition.