The Swans have never beaten Everton in their 18 previous meetings dating back to 1931.
But, having beaten Manchester United at Old Trafford for the first time in the third round last month, Dyer sees no reason why Swansea cannot record another club first.
"Since I've been here history has been created all over the place," he said.
"Everton are our bogey team and we want to stop that rut and get a win against them.
"Seeing our old manager, you always want to do well against them.
"The whole atmosphere of the FA Cup is legendary. Anything can happen and underdogs can go through.
"It's a medal and something to put on your CV so everyone wants to win it."
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