The Bayern head coach delivered an encouraging but careful update after overseeing his side's final training session before travelling to Italy.
"Harry had a good training session today, but we want to wait and see tomorrow morning how he's come through it," Kompany said.
"It's important for us that he's here and can play a role tomorrow."
Kane, England's captain, had missed Bayern's recent 4-1 league victory over Borussia Monchengladbach due to a calf problem, but he looked comfortable and relaxed in training, taking a full part in the session before the squad flew to Bergamo.
Kompany made it clear he would not gamble on the striker's condition, with the tie finely balanced over two legs and Bayern chasing another deep run in Europe.
The Belgian also warned his players to expect a demanding tactical battle against an Atalanta side known for intensity and discipline.
"We're playing against a physically strong team," he explained.
"There are similarities to our game in Dortmund, playing with a back three in possession and looking for runs in behind.
"But the way Atalanta press has been impressive for several years. That's been a big part of their success."
Kompany also pointed to the Italian side's European pedigree and recent performances as reasons for caution.
"They've got experience in Europe and they showed their quality with a convincing win over an impressive Bayer Leverkusen side. They're not an easy opponent. Nobody should underestimate them.
"Every expert knows it can be an interesting tie, but we have our strengths and we know we're facing an Italian team."
Match Context
This will be the first competitive meeting between Bayern Munich and Atalanta in European competition.
Bayern enter the tie in dominant domestic form, sitting 11 points clear at the top of the Bundesliga after an impressive run of results, including major victories over Borussia Dortmund and Borussia Monchengladbach.
Kane's potential return would provide a major boost for Kompany's side, with the striker playing a decisive role in Bayern's attacking system this season.
Newcastle United manager Eddie Howe has challenged his squad to seize a once‑in‑a‑lifetime opportunity by beating Barcelona in their Champions League last‑16 first leg at St James' Park on Tuesday.
Mamelodi Sundowns will face Bundesliga side RB Leipzig in a pre-season friendly encounter in South Africa in May, the club have confirmed.
Hansi Flick has insisted Barcelona will not abandon their identity when they face Newcastle United in the Champions League on Tuesday, warning his players to expect a dangerous and highly motivated opponent.
Arne Slot has said Liverpool's previous experience in Istanbul would help his players handle the "very impressive" atmosphere when they face Galatasaray in the UEFA Champions League last-16 on Tuesday night.
