The Hammers last won at Anfield in September 1963 and Jarvis admitted it would be a remarkable feat to beat the Europa League hopefuls in their own backyard.
Jarvis was instrumental in helping the home side to a 3-1 home victory over West Bromwich Albion on Saturday.
"You don't get any easy games and away to Liverpool will be extremely hard but we're full of confidence after Saturday." the 26-year-old told West Ham TV.
"Let's not talk about (the club's Anfield record), but if we can go there and get a result, it would be a fantastic achievement."
Jarvis reserved special praise for midfielder Gary O'Neil, who has come into the first-team line-up after an injury to Mark Noble, and England forward Andy Carroll after his two goals against the Baggies.
"Gary O'Neil has been fantastic the last few weeks," he added. "He puts in such a shift and doesn't get the praise he deserves.
"The first goal's typical Andy, that's him, getting in the box, getting his head on it. The second one was a great strike. Technically, it's probably up there with the hardest things in football and he nailed it."