Japan international Kagawa had done an outstanding job in replacing injured playmaker Mario Gotze since the start of the year and his absence was felt in Dortmund's nervous and scrappy 1-0 win at Hertha Berlin last week that stretched their unbeaten run to 16 league games.
"It is looking good for Shinji and I hope he can be with us on Sunday," captain Sebastian Kehl told reporters. "Our medical team is doing fantastic work."
"As the longest-serving player at the club now, I am having lots of fun contributing to Dortmund's positive development," Kehl said.
The Ruhr valley club last lost in the league in September and Kagawa's possible return to the squad for Sunday's game would mean a much-needed creative injection in midfield, with the 22-year-old having contributed seven league goals this season.
A win against Hannover, who themselves have gone nine games without defeat, would allow Jurgen Klopp's team to stay at least three points clear of second-placed Borussia Monchengladbach, who are on 46 points, as they chase back-to-back Bundesliga titles.
Bayern's 1-0 defeat to Basel in their Champions League last 16 first leg on Wednesday piled on further pressure as they chase a treble.
"We are stuck in a difficult situation and in this phase we had imagined our game to be different. We must turn things around now," Bayern keeper Manuel Neuer said.
