Collagen is one of the most promising materials for 3D bioprinting because of its distinguished biocompatibility. Cell-laden constructs made of pure collagen with or without incorporated growth supplements support engineered constructs persistence in culture and are perfectly suitable for grafting. The limiting factor for direct 3D collagen printing was poor printability of collagen solutions, especially admixed with cells or tissue spheroids. In our study, we showed that concentrated solutions of native collagen branded Viscoll were effective as bioinks with high fidelity performance. Viscoll containing 20, 30, or 40 mg/ml collagen were used for direct extrusion 3D bioprinting to form scaffolds appropriate to support spatial arrangement of tissue spheroids into rigid patterns with resolution of 0.5 mm in details. Incorporated cells demonstrated sufficient viability. Associated rheological study showed that good printability of the collagen solutions correlates with their increased storage modulus value, notably exceeding the loss modulus value. The proper combination of these physical parameters could become technological criteria for manufacturing various collagen bioinks for 3D bioprinting.