The Sunderland midfielder said Switzerland's "overarching aim" was to beat the defending champions and reach the semi-finals for the first time in their history.
"Regarding the fans, keep dreaming. I am a person who always dreams, and dreams can come true," he said at a pre-match press conference in Kansas City.
"And if we want to fulfil our dreams, you need to work, you need to sweat, you need to give it 100 percent.
"And sometimes you need to do something new. You really need to push your limits if you want to beat Argentina. And I'm convinced my team is ready."
Messi factor
The first question of the media conference at Arrowhead Stadium, which also featured coach Murat Yakin, was unsurprisingly how Switzerland would stop Messi, who is the tournament's joint-leading scorer with eight goals.
"Tomorrow, on the pitch, we will perform as a unit," said Yakin. "We will try to play passes, press high against Argentina, who are the reigning champions.
"Obviously, we will try to do the work on the pitch. We can talk a lot, but in the end, it has to really translate on the pitch. And we do have our solutions."
Xhaka admitted it was not possible to keep the marauding Messi quiet for the whole match but said his men would be "smart".
"I don't know if we can stop him over 90 minutes," he said. "It is going to be difficult.
"However, we have to be very smart. We'll have to be compact, close the gaps, not give him too many spaces. We will try, obviously, to play in position. When we have the ball, he won't be able to act as much."
The Swiss captain, 33, said the match would be one of the highlights of his career, which has included spells with Arsenal and Bayer Leverkusen.
Switzerland have reached the World Cup quarter-finals three times, but not since 1954, when they hosted the tournament.
"After 72 years, to be able to be here with Switzerland and to play against a reigning champion, it just makes me very proud," said Xhaka.
"But I am not here to talk. I want to take the next steps. And we are very close to the end and I am yearning for it.
"I am hungry and now we just need to show how much we really want it on the pitch. We are very well prepared and we need to showcase our mentality and I am sure that we can really bother Argentina."
Yakin dismissed fears that Argentina had been favoured by referees at the tournament after a complaint was filed by Egypt following their defeat by the South Americans in the last 16.
But the Swiss coach said it was important to "hold your ground" against a tough and physical team.
"Argentina are very smart," he said. "Every single duel, for example, is very strong. They really go in hard. There is a lot of passion.
"And if you do not hold your ground, you won't win. And we are very well prepared."
Switzerland will again be without injured midfielder Johan Manzambi, who was outstanding during the group phase.
The Freiburg player, reportedly close to a move to Premier League club Newcastle, did not feature in Switzerland's last-16 match against Colombia, which they won on penalties.
"We tried everything that we could to get him back in peak form," said Yakin. "Unfortunately, he is not able to perform tomorrow."