Everton have now turned to controversial Munich doctor Hans Muller-Wohlfahrt as concern grows for Mirallas, 25.
Wohlfahrt, Bayern Munich's club doctor, has injected patients with animal extracts in the past but has helped many high-profile sportsmen recover.
Moyes admitted: "It's not standard practice. What we are trying to do is find a way of getting people back quicker.
"But sometimes with these injuries, you have to give them a bit of time and TLC.
"I am worried, especially when you are a quick, fleet-footed player like he is.
"It's his first year in the Premier League and there is a little bit of surprise trying to get used to it."