I know with the way Real Madrid enjoyed Ancelotti performance, they don't want to leave him now or anytime soon until they sight a more impressive manager as time goes on. Maybe from next season, they will scout for another manager. Winning the UCL as well as the La Liga was a great winning streak for Real Madrid and it showed their prowess in this season and I'm most convinced that they want to do more next season.
Leaving Ancelotti is something real Madrid may not want to do at this time but just like Liverpool, a time will come when even the team can't help it but to let him go probably for purposes of resting, retiring or on health grounds, either way they are definitely going to have a point where he will leave the team and the team will get to capitalize on his legacy hence look for a replacement for him. Like you did mentioned, if they start scouting for a replacement now it will be a gree idea a d I'm very sure even if they start so early, they are still going to find it really difficult to get a perfect replacement.
A manager that will get them to win the UCL and la Liga at the same time with much ease, is someone Madrid will definitely find difficult to get because such a manager must be very experienced and on a very different level of performance than other coaches who handle other teams, he must have a really different mentality that is geared towards winning mostly and not just to head the team a d having to settle for less, Madrid typical suffered only one loss this season in the la Liga and another two in the champions league this season too.