"We are confident he will be, if not fully fit, so close to it that it will be satisfactory for everyone," Chappell told reporters before the team's departure for Colombo.
India clash with Sri Lanka on August 16 in their opening match of the three-way tournament, which also features South Africa.
Tendulkar, with world record 35 Test and 39 one-day centuries, returned to the squad after being out of international cricket since March due to shoulder surgery.
He had already skipped a One-day home series against England as well as the tour of the West Indies.
"His fitness is improving everyday," said Chappell.
"I thought his batting during the (training) camp here was very good and we have not pushed him very hard at this stage with regard to his fielding, but he is improving every day."
Tendulkar is also the world's leading scorer in the short version of the game with 14,146 runs in 362 matches.
India captain Rahul Dravid said the tri-series was an opportunity for his team to better their record in Sri Lanka.
"We are playing against two very good teams. It is a big challenge but also an opportunity to boost our confidence," said Dravid, whose side were thrashed 4-1 in the West Indies in May.
India have not won a one-day tournament in Sri Lanka in recent times, losing the 2004 Asia Cup final and a triangular series the following year, both times to the hosts.
"The important thing is to score runs on Sri Lankan pitches, which are slow. It is always a challenge because they always play better at home," said Dravid.
"We need to work on certain areas, like batting in the middle order and rotating the strike."