The European Cup remains the one major trophy the Blues have failed to win under Jose Mourinho.
And they open their 2007/08 campaign at home to Rosenberg on Tuesday night.
Terry said: "We're so desperate to win it as a group. It doesn't really come from me. It comes from players within and that will to win comes from inside.
"We're born winners here and that's going to keep us going over the next few years, because we're desperate to win it, and it really sets the tone."