Still, Frank Lampard hasn't communicated that he wants his senior star out despite an aggressive recruitment drive this summer.
Lampard gave Kante the captaincy in the club's most recent friendly and competitive matches due to Cesar Azpilicueta being out injured.
The World Cup winner is currently away on international duty with Blues team-mate Olivier Giroud and is thought to be in good health after an injury-hit last season.
Kante missed almost 50 per cent of his side's matches last term, which became a cause for concern for Lampard, but he kept reiterating his desire to keep the midfielder throughout the season.
“He is an incredible player, I keep saying it and I mean it, he is huge for this club,” Lampard said at the end of June. “He has been huge and he will be for a long time and I am happy with him.
“It is not just about N’Golo. I have got other midfield players and a lot of competition in midfield but at the moment, N’Golo is doing a really good job there.”
Meanwhile, Conte's interest stems from his time at Chelsea from 2016 to 2018, which led to the Blues winning their most recent league title and the FA Cup.
Inter are not able to pay large fees for players as the current market stands, with the club now looking to offload a number of fringe figures before next season starts.
Left-back Emerson Palmieri is another Chelsea player among the Italian club's key targets, with a £26 million ($34m) price tag having been communicated to all parties involved.
However, the Nerazzurri are aiming to negotiate the fee down, with talks likely to progress after Ben Chilwell joined the Blues last week.
Maurizio Sarri had been driving Juventus interest in Chelsea's other defensive midfielder, Jorginho, but the coach's sacking has led his successor Andrea Pirlo to shift focus to other areas in the transfer market.
Having spent over £130m ($172m) already in the transfer market on five players - including RB Leipzig striker Timo Werner, Ajax playmaker Hakim Ziyech and Leicester City's Chilwell - the Blues are still looking to add more players to their squad.
Bayer Leverkusen attacker Kai Havertz's move to Stamford Bridge will break the club's transfer record, with an initial £72m ($95m) payment being agreed for the 21-year-old.
Alongside that move, the Blues are now targeting another goalkeeper to come in and compete for a starting spot with Kepa Arrizabalaga, who struggled for form last season.
Rennes goalkeeper Eduoard Mendy has received a number of approaches from Lampard's side but an offer has yet to be accepted.
West Ham's Declan Rice is another long-term target but he is unlikely to join at this stage with the Hammers so far reluctant to sell their prized asset.