Top scorer Costa and midfield enforcer Kante collected their fifth bookings of the campaign in last weekend's 1-0 win at Crystal Palace – where the Spain international headed home his 13th league goal of the season – to be ruled out of the Boxing Day match at Stamford Bridge.
Both men have been mainstays of the Blues' 11-match winning run that has established a six-point advantage over Liverpool at the summit and their absence leaves Conte with much to ponder.
"For sure, they are two important players for us, this is clear," he told a pre-match news conference.
"But we are working very well this week to try to find the solution to play good football and continue to win and take the three points
"We know that against Bournemouth it won't be easy because it is a very good team with great organisation.
"I have four days to evaluate the situation and to try to find the best solution for the team."
Conte granted his players three days off this week, with Costa and Kante earning an additional 24 hours of recuperation, and the former Italy boss is keen to see some of his squad players take the chance to show their worth.
"I think it is important, this test to see the situation in our squad," he said. "Also to give the possibility of play to some players who, until now, are not playing a lot, or to find some other solution.
"What my eyes see in this week are very important."
Being without Costa could lead to Michy Batshuayi making a first Premier League start after 10 substitute appearances, although Conte will continue to be patient with the 23-year-old Belgium international following his close-season move from Marseille.
"I spoke to Michy in the post-game and I told him it is not easy to arrive in this league and to play when you are a young player," he explained.
"You arrive in a new country. For me it is difficult. It is hard to adapt in this league because it is a very tough, strong and physical league.
"I think Michy is working really well. We must have patience with him to work with him to try and help him to improve."
Whatever alterations Conte settles upon, he suggested Chelsea are unlikely to deviate from the 3-4-3 set-up that prompted their remarkable recovery from a patchy start to the campaign
"I think this team has shown in the past that we can play with different formations," he added.
"I must be honest that when we played with the other formations we did not have these kind of results."