The Hammers sit fifth in the Barclays Premier League heading into Saturday's visit of struggling Crystal Palace and Slaven Bilic's side also face an FA Cup quarter-final replay at home to Manchester United later in the month to secure a place in the final four.
Lanzini said: "I've heard a lot of people talk about whether they'd prefer to win the FA Cup or qualify for the Champions League. I say both, why not?
"That's how strong I believe our squad is. We have to believe we can do it; we have been optimistic all season and look where we are. We're in the latter stages of the FA Cup and close to the Champions League spots, so we have to go for it."
