German newspaper TZ reported the contact between Bayern's scouting department and the player's camp, with Liverpool and Chelsea also tracking Martínez according to GiveMeSport.
City Football Group clubs and Borussia Dortmund were among the clubs present to watch him in person during the tournament.
Martínez operates primarily as an attacking midfielder but can also play in a deeper central role. He assisted Colombia's third goal in a 3-0 semi-final victory over Brazil and faced Argentina in Sunday's final. His performances at youth level have placed him among the most sought-after teenagers in South American football.
Bayern's interest follows a clear pattern. The German champions have built a strong connection with Colombian talent in recent seasons, with Luis Díaz having moved to Munich last summer. Martínez would be a longer-term project — one earmarked to develop into a future number ten.
No deal is imminent and competing interest from multiple clubs means a bidding contest is likely once formal approaches begin.