The Hammers avoided the likes of Arsenal, Chelsea, Manchester United and Manchester City in the fourth-round draw but a trip to Turf Moor promises to be no cakewalk for Sam Allardyce's side.
The Clarets are currently flying high at the top of the Sky Bet Championship and are yet to lose on their own patch this season.
Winger Jarvis knows a number of the Burnley players from his time with Wolves and the 27-year-old is expecting a tough test as the Hammers attempt to move a step closer to Wembley.
"Burnley have done extremely well this season," he said.
"I know quite a few of their players so I know what they are all about. I know Sam Vokes, Michael Kightly, David Jones and Jason Shackell so it will be like friends reunited. But it will be a very tough game.
"A cup tie is always a great game to play in. We're away so hopefully we will have a good turn-out by the fans and give them something to shout about by getting through."
Jarvis came on as a substitute in Sunday's goalless draw at Swansea and is expected to start against the Clarets.
He added: "I want to play in every game so I'm hopeful of playing on Tuesday night.
"It's a chance to try and impress the manager and prove that you should be playing every week.
"When you get a chance you really need to show what you can do and hopefully get yourself in the team."
Jarvis believes the Hammers have a genuine shot at silverware this season - if they can see off the Clarets.
"Of course," he said, "because if you can get a kind draw and get a home tie then you can really see where you can go."