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Sean Dyche's side host Leicester at Turf Moor on Saturday with two points separating the sides and a victory could see either leap out of the relegation zone.
Burnley are propping the division up, but Mee insists that does not faze the hosts as they approach such an important fixture.
"We've had teams come to Turf Moor high in confidence before so there's no reason why we can’t get a result," the defender told the Lancashire Telegraph.
"Anything is possible and we'll be looking to get the points. We've always been confident so there's no reason why that will change.
"It's a big run-in so we've got to enjoy it and hopefully we'll pick up the amount of points that we need."
