Kevin Plank has cultivated a wide circle of celebrities since founding Under Armour Inc. more than two decades ago. As the company has grown from a small startup to a global force in athletic apparel, some have even accompanied the chief executive on the private jet he leases to Under Armour.

Often in recent years, said a number of current and former executives, he has turned to one in particular for business advice: MSNBC anchor Stephanie Ruhle.

The...