Bayern fell to their first league loss of the season 2-1 at Mainz last weekend and are now just four points clear of defending champions Bayer Leverkusen.
Kane's return is good news for Munich, who have missed the England captain's creativity and goals. He had 20 goals and nine assists in 19 games in all competitions before tearing his hamstring in November.
"I'm not going to say whether he will start the match or not, the last training session (Thursday) is important," said Kompany.
"But if everything goes well, he will definitely have a role to play tomorrow (Friday).
"Harry has this science of positioning close to the penalty area. He also helped us a lot in defensive work. He's one of the best in the world in the box -- that's where he makes the difference. There aren't many players who can do that."
Jamal Musiala has stepped up in Kane's absence, with four goals and an assist in all competitions, but the 21-year-old cannot be expected to shoulder the load alone.
"It's always tough," Musiala said of Leipzig, adding "we've had finals against them before and it's definitely a big game -— we lost against them last season."
Musiala's 13 goals and five assists in all competitions ranks just behind Kane, showing how important the Germany-born, England-raised midfielder is for Bayern.
Musiala, who switched international allegiances from England to Germany just after moving to Bayern, credits Kompany for helping him "go up a level this season".
Struggling to kick their title hangover early in the season, Xabi Alonso's Leverkusen have hit form, with seven straight wins in all competitions including knocking Bayern out of the German Cup last 16 in Munich.
A win will ensure a four-point buffer during the winter break. But Leipzig, who sit six points behind Bayern in fourth, have had the advantage over the German giants lately.
Bayern have won just one of their past five games against Leipzig, including two defeats in Munich.
Leverkusen face this season's quiet achievers Freiburg, who sit in fifth place ahead of Champions League sides Stuttgart and Borussia Dortmund.
Third-placed Eintracht Frankfurt are winless in four after a blistering start to the season, but will look to get back on track against derby rivals Mainz.
One to watch: Felix Nmecha (Borussia Dortmund)
A year and a half after arriving as Jude Bellingham's replacement, Felix Nmecha has established himself in the heart of Borussia Dortmund's midfield.
After an injury-hit first year at the Westfalenstadion, where some asked if Dortmund had overpaid for the Hamburg-born, Manchester City academy product, Nmecha has emerged as the perfect link between defence and attack.
Calm on the ball and a goal threat, Nmecha's form has been rewarded with a return to Julian Nagelsmann's Germany squad.
The 24-year-old takes on his former club Wolfsburg on Sunday, with eight-placed Dortmund just one point above their bottom-half-of-the-table opponents.
Key stats
15 - 12th-placed Union Berlin have conceded 15 goals in 14 games. Only league leaders Bayern Munich, with 12, have conceded fewer.
One in 18 - Wolfsburg have won just one of their past 18 league games against Borussia Dortmund dating back to 2015.
0 - Rock-bottom Bochum are the only side yet to win a game this season.
Fixtures (all times 1430 GMT unless indicated)
Friday
Bayern Munich v RB Leipzig (1930)
Saturday
Stuttgart v St Pauli, Eintracht Frankfurt v Mainz, Holstein Kiel v Augsburg, Werder Bremen v Union Berlin, Hoffenheim v Borussia Moenchengladbach, Bayer Leverkusen v Freiburg (1730)
Sunday
Bochum v Heidenheim, Wolfsburg v Borussia Dortmund (1630)
