A message seeking comment was left for a spokesperson for Mangione's lawyers.
Thompson, 50, was ambushed and shot on a sidewalk outside the New York Hilton Midtown as he arrived for his company's annual investor conference.
Surveillance video showed a masked gunman shooting Thompson from behind. Police say the words "delay," "deny" and "depose" were scrawled on the ammunition investigators found at the scene, mimicking a phrase commonly used to describe insurer tactics to avoid paying claims.
Mangione was arrested in Altoona, Pennsylvania, about 230 miles (about 370 kilometers) west of New York City, after a five-day manhunt.