Antonio Conte has no real reasons to walk away after this first success, he has just started. He needs to prove, first to himself, and then to Inter that he is capable of sustaining these kind of results. Winning Champions league would be, ça va sans dire, ideal.
IMO, it would be very stupid to suddenly switch to a new team.
Unless he wants to keep his reputation intact and move on to a new challenge.
Yes they won this season but it was because Juventus was so bad, and because Inter sacrificed their UCL and Europa campaigns.
They played brilliant football at the start but now if you notice, they try to get a goal, then sit back and defend (typical Conte) and try to counter. This is not how you win consistently at modern football.
I mean Inter is a great club and all but are you seriously considering that they are the team with the biggest pocket as well? Think about it, Spurs is missing a manager right now and they are much much richer because of premier league income, so maybe they can offer as much as 2x amount for 5 years? Not that their intention would be to keep him for 5 years if he is unsuccessful, dude could be fired and paid in full as well, but that seems like a possibility.
This is why I think there could be other teams as well, sure Real is not firing Zidane that’s for sure, but there could be other teams that do not have a manager at the end of the season that needs a new manager and has a lot of money that could be paying him a lot of money. If that doesn't happen then it means that he could continue in Inter where he has been very successful and broke Juventus championship streak.