Rossi said Szoboszlai's workload was being managed following back-to-back losses to Switzerland and Germany in Group A, but the Italian did reveal he would make some changes to his line-up.
"We will wait until the 11th hour and assess how everyone is, but there's no real concern over Szoboszlai at this stage of the competition," Rossi told a press conference on Saturday.
"At this stage of the season, it was a very long campaign for him in particular, what matters most now is rest and recovery."
"There will be a couple of change but that doesn't come down to bad performances by any means," added Rossi.
"It's simply because we believe we can have a bit more freshness in the side."
Hungary arrived at the Euros with increased expectations after a 14-match unbeaten run between November 2022 and March of this year. They also beat England home and away in the last UEFA Nations League.
But a 3-1 defeat by Switzerland in their opening game in Germany set the tone for a difficult campaign, with a subsequent 2-0 loss to the tournament hosts leaving them bottom of the pile and without a point.
"I think that this unbeaten streak raised the expectations. I can say we were no exception. We also started off expecting more points at this stage of the tournament," said defender Endre Botka.
"Now we see that in the last two games we didn't do as we expected. At times like that we have to go back to the basics and the things that were working in the past."
The game in Stuttgart will be the first competitive meeting between Hungary and Scotland, who have one point from two games after bouncing back from a 5-1 drubbing by Germany to draw 1-1 with Switzerland.
"There's no alternative for us but to win if we want to continue our progress," said Rossi.
"We know this is a decisive game both for us and them. The pressure is equally on for both us and Scotland."
