Howard and Everton welcome Fulham to Goodison Park on Friday evening, with the goalkeeper firmly of the belief Dempsey is the man they need to stop to give themselves the best chance of winning.
Dempsey is the top scorer for Martin Jol’s side this season with nine league goals, something Howard is well aware of following the attacker’s hat-trick against Newcastle, but he believes the club has been relying on the former New England star more and more each year.
Speaking to evertontv, Howard said: "Without any disrespect to Fulham, I think Clint's been their best player for quite a while.
"It seems year after year they begin to rely more and more on his presence, on his goals and on his leadership.
"I know Clint has been on a wonderful scoring run but hopefully we can keep him out and keep him quiet."
Dempsey scored a hat-trick in the third round as Fulham overcame League One side Charlton Athletic 4-0 at Craven Cottage.
The American has scored 15 times in all competitions this season, including three in the Europa League.