This study was sought to investigate the feasibility of using smartphone-based breathing sounds within a deep learning framework to discriminate between COVID-19, including asymptomatic, and healthy subjects. A total of 480 breathing sounds (240 shallow and 240 deep) were obtained from a publicly available database named Coswara. These sounds were recorded by 120 COVID-19 and 120 healthy subjects via a smartphone microphone through a website application. A deep learning framework was proposed herein that relies on hand-crafted features extracted from the original recordings and from the mel-frequency cepstral coefficients (MFCC) as well as deep-activated features learned by a combination of convolutional neural network and bi-directional long short-term memory units (CNN-BiLSTM). The statistical analysis of patient profiles has shown a significant difference (p-value: 0.041) for ischemic heart disease between COVID-19 and healthy subjects. The Analysis of the normal distribution of the combined MFCC values showed that COVID-19 subjects tended to have a distribution that is skewed more towards the right side of the zero mean (shallow: 0.59±1.74, deep: 0.65±4.35, p-value: <0.001). In addition, the proposed deep learning approach had an overall discrimination accuracy of 94.58% and 92.08% using shallow and deep recordings, respectively. Furthermore, it detected COVID-19 subjects successfully with a maximum sensitivity of 94.21%, specificity of 94.96%, and area under the receiver operating characteristic (AUROC) curves of 0.90. Among the 120 COVID-19 participants, asymptomatic subjects (18 subjects) were successfully detected with 100.00% accuracy using shallow recordings and 88.89% using deep recordings. This study paves the way towards utilizing smartphone-based breathing sounds for the purpose of COVID-19 detection. The observations found in this study were promising to suggest deep learning and smartphone-based breathing sounds as an effective pre-screening tool for COVID-19 alongside the current reverse-transcription polymerase chain reaction (RT-PCR) assay. It can be considered as an early, rapid, easily distributed, time-efficient, and almost no-cost diagnosis technique complying with social distancing restrictions during COVID-19 pandemic.