High-scoring Germany face a powerful Ivory Coast side at the World Cup on Saturday with the winner guaranteed a place in the last 32, while Sweden can also book their ticket.
Those three nations can join co-hosts the United States and Mexico who are already through.
Germany thrashed debutants Curacao 7-1 in their opener and would be confirmed as Group E winners if they defeat Ivory Coast in Toronto and Ecuador fail to beat Curacao in Kansas City.
Progressing to the knockout round would be a relief for the Germans who astonishingly have failed to reach that stage since they won their fourth World Cup in Brazil in 2014.
So tight are the margins that Ivory Coast could lock up their place in the next round too, if they beat the Germans.
Nagelsmann said his team had to be prepared for Ivory Coast's athleticism.
"Their speed is one of their biggest strengths and that's what I think they do best," he told reporters, highlighting the French-born Ivorian winger Nicolas Pepe.
"During the last game, he was everywhere," Nagelsmann said of Pepe.
Sweden face the Netherlands in Houston knowing that a win will secure a place in the knockout round – an extraordinary turnaround for the Scandinavians who only qualified for the World Cup through through the Nations League, essentially the back door.
Coach Graham Potter warned that Sweden striker Alexander Isak will get "stronger and stronger" as the tournament goes on.
Isak had a poor season by his standards, interrupted by frequent injuries, after Liverpool paid Newcastle United a British record £125 million ($165 million) for him.
He made a strong start to the World Cup though as the 26-year-old scored one goal and set up two in the 5-1 thrashing of Tunisia.
"Alex has had a season that has been interrupted," Potter said. "Most football players would say they need a certain amount of time and games to get up to top, top level, so we've had to try to build Alex up. I think there's more to come from him."
1 000TH GAME
History will be made in another of Saturday's games as Japan face Tunisia in Monterrey, Mexico for the 1 000th game at a World Cup.
Hajime Moriyasu warned his Japan side they will need to match the intensity of a Tunisia team fired up by the introduction of coach Herve Renard after Sabri Lamouchi became the first coach in World Cup history to be sacked after one game.
On Friday, the United States marched into the knockout round with a 2-0 victory over Australia in Seattle.
A day of raucous celebrations for the co-hosts got even better when Paraguay's 1-0 win against Turkey confirmed that the US would clinch top spot in Group D, ensuring a theoretically easier draw in the last 32.
A Cameron Burgess own goal in the 11th minute and a headed effort from Alex Freeman two minutes before halftime sealed a comfortable three points for Mauricio Pochettino's USA side, who have won the group with a game to spare.
After an unconvincing build-up to the World Cup, the Americans have made a dream start to the tournament with Friday's victory following a stylish 4-1 demolition of Paraguay in their opener.
"It was a fantastic game again, very good first half," Pochettino said. "I think we dominated the game against a very tough team.
"When the draw happened in December I thought it was going to be a really difficult, a really tough game."
In other games on Friday, Brazil took control of their destiny in Group C with a 3-0 victory over Haiti that ended the Caribbean nation's chances of progressing. Haiti join Turkey in exiting the tournament.
Two goals from Matheus Cunha and a Vinicius Junior strike sealed an easy win for the Brazilians in Philadelphia.
Brazil are now level on four points with Morocco, but lead the North Africans on goal difference.
Morocco secured their first win of the tournament on Friday with a 1-0 defeat of Scotland at Foxborough.
Ismael Saibari scored the games's only goal, lashing home an angled strike in the second minute.
Morocco face Haiti in their final Group C game on June 24, while Brazil take on the Scots in Miami.
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