Tottenham trail last year's champions by six points with just under half of the season remaining and Dempsey is confident the Londoners can catch Roberto Mancini's expensively-assembled side.
"That's the goal," the Spurs forward said when asked if finishing second was a realistic target.
"Everybody wants to be pushing for great things and doing something special in their careers. We have the quality in our team and there's no reason why we shouldn't think that.
"We need to continue on this good run of form and get as many points as possible. You want to keep your feet on the ground and know there's a lot of hard work to put in if you want to accomplish your goals."