Industries across the globe are under growing pressure to rethink and redesign their supply chain operations to maintain their competitive advantage. The supplier selection process in supply chain management holds a pivotal position in its exploration of new strategies to stay competitive in global markets. This study considers supplier selection with two different strategic perspectives, including lean and agile. Selecting suppliers based on their leagile practices helps the focal industries to make their supply chain operations healthier, especially if the focal industry is a major supplier of multinational companies. China is considered as a case context in this study with the application of textile sectors since this country occupies the top position with regard to exports. The common criteria involved in leagile supplier selection were collected from existing literature resources and were fine-tuned with insights from field experts. Further, the case industrial managers also assisted with the evaluation of the influential criteria for the leagile supplier selection process. Based on the replies and the assistance of a decision-making trial and evaluation laboratory tool, the most influential criterion and interdependencies among other criteria were identified. This study helps industrial managers to evaluate their suppliers based on the resultant influential criterion and, further, it strengthens the global supply chains with agility and robustness.