The 27-year-old centre-back has long been hailed as one of Serie A’s top enforcers, both for his current side and former team Udinese.
Scouts from the Premier League champions have been assessing the speedy South American of late, and are believed to have been impressed with what they have witnessed.
Despite him having only signed for the San Siro giants earlier this year, Moyes is hopeful that he can launch a successful January raid for his services.
Zapata is seen as an ideal long-term replacement for Rio Ferdinand, with the Milan star also a technically adept and skilful defender.
Moyes’ top target remains Porto’s Eliaquim Mangala, but the Scot is worried about being dragged into a bidding war for the Frenchman, who is also wanted by Barcelona, Monaco and Chelsea.
Zapata has been impressive at international level as well as for his club, and is regarded as a key member of Colombia’s set-up.
England could potentially face the Tricolor – who are ranked as the fourth best national team in the world by FIFA – at next summer’s World Cup if they both advance from their respective groups.