Keller also defended the atmosphere generated by supporters across the tournament and questioned FIFA's use of hydration breaks.
Keller, one of the most accomplished players in American soccer history, earned 102 caps for his country and represented the USA at four World Cups between 1990 and 2006.
The former goalkeeper also enjoyed a lengthy career in English football, featuring for Millwall, Leicester City, Rayo Vallecano, Tottenham Hotspur and Southampton before finishing his playing days in Germany and Major League Soccer. His spell at Tottenham in particular established him as one of the most respected American players to play in the Premier League era.
Now working as a broadcaster and analyst, Keller has been impressed by the United States' opening 4-1 victory over Paraguay but believes expectations should remain realistic despite the excitement surrounding Mauricio Pochettino's side.
Speaking to Football Presse, Keller said the Americans should focus on progressing through the knockout stages rather than looking too far ahead.
"I think if they finish high, they play well in the next two games, finish first in the group, have a favourable draw in the round of 32, get to the round of 16 and then let's see who the opponent is," Keller said.
"I think if you're realistic, are you telling me that the United States is one of the eight best footballing nations in the world?
"Don't get me wrong, we can beat anybody on the day and we've proven that in the last 30 years.
"But once you start to get to knockout stages, you understand that the big boys that have figured it out, that have gelled, that have the right team spirit and chemistry, when they start getting to quarter-finals, it gets serious."
For Keller, the immediate priority remains navigating a difficult group that still contains Australia and Türkiye.
"Let's finish the opening round strong. Let's look at that round of 32, do the business there and then we'll have another conversation in the round of 16."
The 56-year-old's perspective is shaped by experience. Having appeared at four World Cups, Keller has witnessed football's biggest tournament evolve dramatically over the last three decades.
Asked which tournament stood out most, he pointed to Germany 2006 because of the atmosphere generated by supporters.
"For different reasons, Germany in 2006 was the first time I really saw a level of support for almost every match," he explained to Football Presse, on behalf of England to win World Cup odds.
"That was the first time I really noticed the US travelling fans."
Keller recalled the Americans' group-stage meeting with Italy in Kaiserslautern as a particularly memorable occasion.
"We had 20,000 American fans, 20,000 Italian fans, 10,000 neutrals and it was an unbelievable atmosphere."
The former goalkeeper also dismissed concerns raised before this year's tournament about attendances and fan engagement.
"There was negativity before the tournament, like the fans aren't going to show up and ticket prices are too expensive," Keller said.
"But once this thing kicked off, it's been tremendous."
While Keller has enjoyed much of what he has seen, he is less convinced by one aspect of the competition.
The former USA international believes some of FIFA's hydration breaks have little to do with player welfare.
"I'm a fan of a hydration break. I'm not a fan of a commercial break," he said.
"There was absolutely zero reason for a hydration break in the second half.
"It's supposed to be a high of 73 in Seattle on Friday and I guarantee you there will be two hydration breaks.
"The fact that they've basically snuck in this 'it's going to be hot in America, so we'll have these hydration breaks' tells you it's not a hydration break, it's a commercial break."
As the United States prepare for the next stage of their World Cup journey, Keller's message is clear: enjoy the encouraging start, but keep expectations grounded until the bigger tests arrive.