Kompany, 39, and his side are looking to be running away with the Bundesliga title and are among the favourites to win the Champions League.
Several reports have suggested that he could be the man to replace Pep Guardiola at former club Man City should the legendary Spaniard leave in the summer.
Speaking to Absolut Bayern, Eberl has dismissed the rumours, saying: "Let them have a go; he’s under contract until 2029.
"Even though he’s only turning 40, he’s already one of the very best in the coaching profession. Because he’s a very astute, intelligent person.
“Please emphasise the word ‘person’! People have always had respect for him. But he makes that respect grow every day. Simply by being himself.
“He brings the experience he gained as captain of a top-flight team to bear before every match. That quality is fantastic; his composure does us a world of good.”