According to the paper, speculation about Apple's plans for fingerprint recognition began last year when the iPhone maker bought biometric security firm AuthenTec for 235 million pounds.
Earlier this month, KGI Securities analyst Ming-Chi Kuo said his firm expected the results of that takeover to be revealed this year with the new iPhone 5S.
Samsung has had a "Face Unlock" feature in its phones since last year's Galaxy S3.
However, the phone's camera would often unlock if it recognised a photograph of the owner.
The firm said the feature has been improved in the Galaxy S4, released in New York last week.