The duo have been linked with a move away from Goodison Park this summer, with Manchester United seeing an offer for England international defender Baines rejected recently.
Belgium midfielder Fellaini has also been mentioned as a possible transfer target for several leading Premier League clubs after his impressive displays for the Merseysiders.
But Moyes insists he is paying little attention to the on-going rumour-mill and claims he takes interest in any of his squad as a compliment.
He told Sky Sports News: "This is the moment of having speculation, having talks and clubs looking around. I see it as a real compliment - you don't get that if you don't perform well.
"We are Everton and we want to keep our best performers and we have got our own aims and that is very clear.
"We are not losing any sleep over that (speculation). We are really focused and trying to work as well as we can as a group, making sure that every day counts towards where we want to get.
"The attitude of the group is exceptional and that is what excites me, looking forward to tomorrow and making sure we grow day by day."
Martinez was speaking after his side ran out 4-1 winners in their pre-season friendly at League Two side Accrington.