I do not think Chelsea will budge, they usually do not give players above thirty anything more than a year or two contract extension, and i don't think Kante's case will be different, but then there is a new management in charge like you said and we would see how they handle this situation, Kante has served the club very well since his move from Leicester, and a three-year extension might be no more than what he deserves. Having said that, i am pretty sure various other clubs will be monitoring this situation right now, and if there is a breakdown in negotiations, some of them will not fail to offer Kante a contract he might not be able to say no to.
Agree with what you said, he is one of the players who has an important role at Chelsea at the moment although indeed this season his role is still not visible but indeed he can be one of the players to be reckoned with when the team recovers.
Regardless of his age, he is actually quite reasonable when his contract duration is three years if this can be realized.
I do not get why people consider him "aging" though, Benzema was 35 years old when he scored all those goals last year and managed to win the UCL title and La Liga title with Real Madrid. Kane is 31 years old and a 3 year contract would mean that he would be 34 by the time it ends, or 35, those are still doable numbers and not aging if you ask me, not in this football world at least.
I get that some people remember the old days when players retired at 35 or even ealrier but people like Kante take care of their body nowadays and can play even as old as 40 years old, so I do not think that 34-35 would be that bad. Plus, he isn't some role player, dude is their best player and they should do whatever it takes to keep them in check.
I think that the average longevity of players has gone up by at least 3 to 4 years. Because if you look at some legendary players from the past almost all of them retired before the age of 32 or 33. However, nowadays there are some players like Benzema who start to flourish after 35. If you look at
, he is 37 and still is one of the most talented midfielders at this moment. So we can surely say that N'Golo Kanté will be able to play till he is 37 or 38 at the highest level. Although we will need to wait and see what the new Chelsea management thinks about him and whether they renew with him or not.