Gyan scored the winner in extra time when Ghana sent the United States tumbling out of the World Cup for the second successive tournament in South Africa four years ago. (Agencies)
"It's going to make the game more difficult," said Gyan.
"They are coming for revenge. Mentally, they don't want to lose to us for the third time. It's going to make it very interesting and difficult for us. But we're ready to go out and give our all tomorrow," he said.
Gyan also missed the penalty awarded against Uruguay for Luis Suarez's infamous goalline handball in Johannesburg that would have made Ghana the first African side to reach the last four at a World Cup.
That they lost the subsequent penalty shootout has not reduced the expectation in Ghana that the Black Stars can go one better in Brazil.
"Back home expectation is high. In 2006 we got through the group stage and in 2010 we got to the quarter-finals," Gyan said.
"Now the people back home believe we can do more. That's pressure but sometimes pressure is a good thing. We believe in ourselves, we are confident in our quality," he said.
While wary of a United States team 24 places above Ghana in the FIFA rankings, Gyan is convinced his side has more raw talent than their opponents.
"Ghana is the more talented team," he said. "We have got a lot of talented players who are coming up and most of them are playing well for their clubs. I think we've got the youngest team in the tournament,” he added.
"The United States are a dangerous team but we don't think about the opponents but we think about ourselves."
Coach Kwesi Appiah said the abundance of talent at his disposal sometimes gave him selection headaches and said he would not choose his starting line-up until after the final training session on Sunday.
Gyan's usual strike partner Abdul Majeed Waris, who suffered a thigh injury in their last warm-up against South Korea, had been back in training for the last two days and could start against the Americans, Appiah added.
With Germany and Portugal completing Group G, Ghana are considered to have a slim chance of getting out of the group. That suits Gyan just fine.
"We know that's what everyone thinks about Ghana, that the other teams are favourites, which is statistically right," he said.
"But so far we've seen a lot of surprises in the tournament and we enjoy being underdogs. We need to make sure we be ourselves and do the right thing," Gyan said.
Gyan scored the winner in extra time when Ghana sent the United States tumbling out of the World Cup for the second successive tournament in South Africa four years ago.