Leicester offered Kante a new £100,000-a-week (NZ$185,000-a-week) contract to stay at the King Power Stadium, but the player is keen to be part of Conte's Chelsea revolution - even though it means giving up the prospect of playing Champions League football in the coming campaign.
Kante becomes Chelsea's second summer signing following the arrival of striker Michy Batshuayi, but Conte wants more players before the start of the new season.
Chelsea have already made a bid for Napoli central defender Koulibaly, but their pursuit of the Senegal international has been complicated by strong rival interest from Everton that has driven up the price.
Everton are prepared to go head-to-head with Chelsea for Koulibaly, who they see as the perfect replacement for John Stones, but the 25-year-old is understood to favour a move to Stamford Bridge.
Kante becomes Chelsea's second summer signing following the arrival of striker Michy Batshuayi, but Conte wants more players before the start of the new season.
Chelsea have already made a bid for Napoli central defender Koulibaly, but their pursuit of the Senegal international has been complicated by strong rival interest from Everton that has driven up the price.
Everton are prepared to go head-to-head with Chelsea for Koulibaly, who they see as the perfect replacement for John Stones, but the 25-year-old is understood to favour a move to Stamford Bridge.
Koulibaly is said to be hoping that Chelsea can agree a deal with Napoli, but could still be convinced to go to Goodison Park if Everton outbid their rivals and the Blues ultimately look elsewhere.
Everton want to be sure of securing a replacement for Stones before sanctioning his move to Manchester City and are holding out for a £50m (NZ$92.5 million) fee for the 22-year-old, who was last year the subject of four failed bids from Chelsea.
Conte, who has flown with his squad for a pre-season training camp in Austria and takes charge of his first game against Rapid Vienna on Saturday, still wants another new striker, but his pursuit of Alvaro Morata is proving to be difficult with Real Madrid playing hardball over the Spaniard's future.
Chelsea have failed with one bid for Morata, with Real claiming they will not sell the 23-year-old unless a club matches their £62m (NZ$114.7 million) valuation of him.
Such a hard stance puts the emphasis on Morata to push for a move away from Real, with Chelsea now waiting to see how the situation develops.
Speaking of Chelsea's need to make signings, Conte said: "I am sure that in the coming days we can reach our target to reinforce the team to go closer to the other teams that now seem to stay higher in the table compared to Chelsea. In the coming days, we can buy one, two, three players. Players that can reinforce us for the season as it will be very, very tough."
