Kagawa's campaign last term was blighted by a serious injury while on international duty with Japan at the Asian Cup in January, ruling him out of the remainder of Dortmund's fixtures bar the last game of the season.
And while he has since make a full recovery, he has taken longer than his team-mates in reaching the levels of fitness required with the season just five days away.
Despite playing 85 minutes for Dortmund in Saturday's 3-0 DFB-Pokal win over Sandhausen, where he scored a goal and laid on an assist, Kagawa insists he still has some way to go before he is satisfied with his fitness levels.
"I feel that I am not fit yet because it was a tough pre-season schedule, which included the tour to France," Kagawa said following Saturday's game.
"Even though I will have a game with the Japan national team [against South Korea on August 10], I have a week to rest myself before the league starts [this weekend]."
Kagawa also expressed caution ahead of Japan's World Cup qualifying campaign, having been handed a tricky group comprising of Uzbekistan, North Korea and Syria.
"Every team will be a tough opponent. It is hard to win in Asian football.
"We have to be on alert will all opponents."
Dortmund kick off the defence of their Bundesliga title this Friday at home to Hamburg.