Howard is set to come up against his compatriot on Friday when their respective clubs go head-to-head at Goodison Park in the FA Cup fourth round.
Dempsey has been in scintillating form of late, with two hat-tricks in his last three games taking his tally for the Cottagers this season to 15 goals, and Howard is in no doubt that the forward is someone the Toffees will need to pay special attention to.
"Without any disrespect to Fulham, I think Clint's been their best player for quite a while," Howard told evertontv.
"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."
The match is likely to generate significant interest across the Atlantic given that another American star, Everton loan signing Landon Donovan, could also feature.
Howard views Dempsey and Donovan as the "key cogs" for the US national team and has hailed the impact the latter has made over the last few weeks since joining the Toffees for a two-month stint - as he did in January 2010.
"I would hope there'll be a big American interest," Howard said.
"They are two of our biggest marquee players, not because of their marketability, how they dress or the way they look but because they are our best players bar none, and from a US national team standpoint they're the key cogs.
"We need to have Landon Donovan and Clint Dempsey at their best to make waves, win competitions, qualify for World Cups and so on.
"Landon has been a huge positive for us.
"He's put in some really solid performances and one thing about Landon is he's very aware of what goes on on a football field and he reads situations and how he can best provide for the team in those situations.
"He's very clever in that regard and talent-wise he's up there with the best. He's done well.
"We always kind of knew him coming back was a great situation for him, a great situation for us and that it would be seamless, because he's been here before and understands the landscape."
