While coach Jurgen Klopp has played down title talk as far too premature, forward Kagawa told Japanese reporters what many in Germany see as more and more possible.
"If we continue approaching every game with such focus then we could again have something this summer that our fans can smile about," said the 22-year-old Japan international, who scored twice in their 3-1 win over Hoffenheim last week.
Dortmund, level on 40 points with leaders Bayern Munich and Schalke 04, have kicked off the year with two straight wins and eight goals, stretching their unbeaten run in the league to 13 matches with their last defeat coming back in September.
Kagawa, who missed half of last season with a broken leg, has also successfully filled the gap left by injured Germany international Mario Gotze, who will be out for at least another month.
With Paraguay international Lucas Barrios deciding to stay on despite several offers after losing his starting spot, Dortmund's front-line, completed by Polish international Robert Lewandowski, who has netted 14 times, remains a lethal threat.
"I am personally very happy with Lucas' decision. From our side there were never any attempts for a transfer," Klopp told reporters.
Title rivals Bayern have looked less sharp since the restart and Saturday's trip to improving Hamburg SV poses a stiff challenge.
Hamburg, with one defeat in their last 11 games, have lifted themselves off the bottom spots under coach Thorsten Fink, who won four Bundesliga titles as a Bayern player.
"Those were great times but now I am at Hamburg and on Saturday we will step on the gas," Fink told reporters. "We can play freely, we are the outsiders and they want to be champions. Maybe we can spring a surprise."
Schalke will be looking to remain in the top group with victory over Mainz 05 on Saturday.
