Despite having missed the whole of the season with an ankle injury, the midfielder is thought to be on coach Stuart Pearce's shortlist for the tournament.
However, Rosicky believes that the 20-year-old needs to focus his attention on getting back to full fitness.
"The Olympics would be the worst idea for Jack," Rosicky told the Gunners' official website. "When a guy has not played for year, he needs a good and slow preparation to start the season.
"Once he is fit he can think about the national team.
"It is not that I don't want him to go to the Olympics. It is just that he has other priorities than that."
Rosicky is expected to feature for Arsenal when they travel to Stoke City in the Premier League on Saturday.