After finding out about Milan's sacking Pioli recently I'm curious about who they will bring for the job. I couldn't find any news related to a candidate yet. Does anyone suitable comes to your mind? 
I only remember Pochettino who is available after getting sacked by Chelsea recently. He hasn't managed an Italian team in his career yet but there is always an opportunity to try a new adventure.
If Mourinho didn't sign a deal with Fenerbahçe then maybe there might have been a chance for him to return to Italy. But Milan seems like they have a strict policy with bringing an Italian manager. Most of their managers so far have been like that so let's see who it will be this time.
I don't think Milan has fired Pioli and maybe this is the final step they can take before next season starts. We know that Milan's record is not good enough even though they managed to finish in 2nd place in the standings and if they had not dropped points in some of their matches then they would have been much more reliable as Inter's competitors in winning the Scudetto.I only remember Pochettino who is available after getting sacked by Chelsea recently. He hasn't managed an Italian team in his career yet but there is always an opportunity to try a new adventure.
If Mourinho didn't sign a deal with Fenerbahçe then maybe there might have been a chance for him to return to Italy. But Milan seems like they have a strict policy with bringing an Italian manager. Most of their managers so far have been like that so let's see who it will be this time.But it's all over and they really have to do something different next season. Regarding the available coaches, I don't think Pochettino will be suitable to handle the Italian team and if possible they could contact Conte who is also still available on the market. I think an Italian coach will still be Milan's main choice rather than a coach from another country.
and on the one hand, the quality of Inter players is really very different from the talent and teamwork which is far superior to Milan, while Pioli has actually provided the right strategy and contributed to being the best team, but the fact is that whatever Milan does is not enough to compete with Inter.
regarding the coach who might be Pioli replacement and suitable for Milan, it is actually not Conte, because I heard from several people on this forum providing sources that Conte would prefer to be with Napoli and seems to have agreed to work together next season.
Mourinho is one of the experienced coaches who might be more suitable to replace Pioli, even though Pioli is still convincing to become Milan coach, but if Milan management really wants to find a new coach, it looks like Mourinho could be one of the candidates for a new coach who can bring Milan to the next level.