When it comes to Pochettino's future it seems like Manchester United and Bayern Munich both are interested. At least most recent rumours say that. If Manchester United parts ways with Erik ten Hag soon then I hope they would be patient with their new manager and take the right steps with the transfers as well. I don't know how many times I will say this but it is really important for them to recover.

Bayern Munich seems in close contact with Kompany recently though. But maybe they are thinking of Pochettino as Plan B who knows. Recent updates I see on the internet are increasing the probability of seeing Kompany as their new manager.
I haven't heard any news about Manchester United's interest in Pochettino after Pochettino officially parted ways with Chelsea. Because so far I have seen that Erik Ten Hag's position seems to be still trusted by management even though we know that he had a bad performance with Manchester United. I don't know why this happened, because if we compare it, Chelsea also released Pochettino even though he could show improvement.
It seems that Manchester United is quite comfortable with this coach, and I think this is because he always agrees to management's wishes, or he is a coach who does not disobey. If this is true then this is actually a bad thing for the team itself, because it means there is something unhealthy about management in managing the club.
However, I hope this is just my feeling, I hope the things I said above don't happen, and when Manchester United retained Erik Ten Hag it was purely because they had evaluated it, not because of anything else.