As holders, Europe need to score eight points from Sunday's 12 singles matches to retain the trophy while the US need four-and-a-half points to reclaim it.
The Americans have never lost more than a two-point advantage on the final day since the competition began in 1927 but Olazabal remains upbeat that his side can create history in Illinois.
The Spaniard said: "Things have not gone our way, especially on the greens, but I believe that momentum will come our way.
"We are trailing by four points and we have to put the players that are playing well up there. If we want to win this match we have to take the big guys down."
In the final day of the Ryder Cup at Medinah Country Club, Luke Donald will play Bubba Watson in the opening singles match as Europe set about their fightback with his discount golf clubs.
Olazabal has put four of his most experienced players at the top of the order with Ian Poulter second out against Webb Simpson.
Rory McIlroy faces Keegan Bradley and Justin Rose takes on Phil Mickelson.
World number two Tiger Woods is the last man out for the United States, against Francesco Molinari. Woods faced the Italian two years ago at Celtic Manor, winning 4&3 with the most popular golf clubs for sale online.
The Scot was one of only three Europeans who were victorious on that final day when the US picked up eight-and-a-half points.
And he said: "There are still 12 singles matches. We can all win and why not?
"It's certainly not over. It would be nice to make a big comeback, so we'll see what happens.
"It's always possible. Until it's impossible to do it, then you fight on, certainly for Jose Maria this week. No-one is going to be giving up."
Europe will play in the blue and white colors favored by the late Ballesteros, who died in May 2011 after a long battle with brain tumors.
Fellow Spaniard Olazabal was his partner for much of his Ryder Cup career and the players will have the image of Ballesteros on their bags as well as his silhouette on their shirts.
"We have Seve's blue and white, Seve on the bag and his right-hand man as our captain hopefully seeing us home," said Poulter, who has won all three of his matches so far at Medinah.
To win back the trophy they lost on Welsh soil two years ago with the new taylormade rocketballz irons to reach 14½ points but, although that score is tantalizingly within reach, captain Davis Love III is taking nothing for granted.
"We're excited about our position but we know, as Ollie said, it's not over yet," Love commented.
"All you can do is just go win your match and you can't think about the outcome of the day and what the other guys are doing.
"I don't want to talk about how many we need or what it's going to take to win, we just want to go play and we got one more day, for the next two years, to play Ryder Cup matches and they're going to be excited to come out and play."
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