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Laboratory medicine plays a fundamental role in the detection, diagnosis and management of COVID-19 infection. Recent observations of the morphology of cells circulating in blood found the presence of particular reactive lymphocytes (COVID-19 RL) in some of the infected patients and demonstrated that it was an indicator of a better prognosis of the disease. Visual morphological analysis is time consuming, requires smear review by expert clinical pathologists, and is prone to subjectivity. This paper presents a convolutional neural network system designed for automatic recognition of COVID-19 RL. It is based on the Xception71 structure and is trained using images of blood cells from real infected patients. An experimental study is carried out with a group of 92 individuals. The input for the system is a set of images selected by the clinical pathologist from the blood smear of a patient. The output is the prediction whether the patient belongs to the group associated with better prognosis of the disease. A threshold is obtained for the classification system to predict that the smear belongs to this group. With this threshold, the experimental test shows excellent performance metrics: 98.3% sensitivity and precision, 97.1% specificity, and 97.8% accuracy. The system does not require costly calculations and can potentially be integrated into clinical practice to assist clinical pathologists in a more objective smear review for early prognosis. [ABSTRACT FROM AUTHOR]