Mucha, 28, has kept goal in both Everton's pre-season friendlies so far, with regular no.1 Tim Howard given extended leave after his involvement with the US national team at the Gold Cup.
Chris Woods has urged Mucha to take the chances he will be given in pre-season, telling evertontv: "I think he has got to look at it and see that it is a chance to show what he can do on the team.
"That is what he needs to do and when Tim gets back with us he will be wanting to get started as well. Jan played well against Philadelphia but unfortunately we didn't clear it and it ended up in the net. But generally we were pleased."
Woods is also working with academy product Adam Davies in America, and commented: "Adam is 19 now and he is well accustomed to the work that we do. The goalkeepers push each other along and it has been tough because it's been 95 degrees out there.
"Hopefully it helps, the experience that Tim has, Jan has and that I have is useful and we all help each other."