Despite the fact that squab is consumed throughout the world because of its high nutritional value and appreciated sensory attributes, aspects related to its characterization, and in particular genetic issues, have rarely been studied. In this study, meat traits in terms of pH, water-holding capacity, intramuscular fat content, and fatty acid profile of the breast muscle of squabs from two meat pigeon breeds were determined. Breed-specific differences were detected in fat-related traits of intramuscular fat content and fatty acid composition. RNA-Sequencing was applied to compare the transcriptomes of muscle and liver tissues between squabs of two breeds to identify candidate genes associated with the differences in the capacity of fat deposition. A total of 27 differentially expressed genes assigned to pathways of lipid metabolism were identified, of which, six genes belonged to the peroxisome proliferator-activated receptor signaling pathway along with four other genes. Our results confirmed in part previous reports in livestock and provided also a number of genes which had not been related to fat deposition so far. These genes can serve as a basis for further investigations to screen markers closely associated with intramuscular fat content and fatty acid composition in squabs. The data from this study were deposited in the National Center for Biotechnology Information (NCBI)’s Sequence Read Archive under the accession numbers SRX1680021 and SRX1680022. This is the first transcriptome analysis of the muscle and liver tissue in Columba using next generation sequencing technology. Data provided here are of potential value to dissect functional genes influencing fat deposition in squabs.