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Literally before Manchester United can come back to good form now it will absolutely take a lot of time no matter the coach they would want to hire now so that is it because to build Manchester United now is a very big task for any coach at all because the first work will be to build the mindset of the players to be able to align with the coach, having a good relationship and understanding between the Coach and the players is very important. Manchester United allowing Eric Ten Haag to still continue next season might cost the club chaos because I don't see him making any difference next season but retaining him could be if he makes some improvements for the club if not I see no reason retaining him when he is not doing well.
It is not easy to achieve the same glory as in the past as long as Manchester United does not have a number of good and quality players in its squad. Manchester United certainly has to improve from A to Z, where the coach and main squad must be a priority for improvement. The problem is that of course it takes time and patience, but people continue to put Manchester United under pressure.
Manchester United need to get good defenders, they also need to get great midfielders, then they also need productive strikers. This squad needs refreshing which will likely cost hundreds of millions of dollars, but to return to its best performance every team needs time.
About Chelsea improving from next season is not certain because they are literally facing same problems of coach with Manchester united so until they sign a coach that can rebuild the team again, they might even get worst next season. I assume you want to say that if Manchester city finish below 7th position instead of below 7th position but however, regardless of their current drop in performance, they can still finish within the 6th or 7th position before the league ends.
Chelsea is the same as Manchester United. They need a lot of budget to build a great squad, not just about expensive players who are unable to make a good contribution. Both teams have been equally bad in recent seasons, but if they truly have a long-term project then I'm sure improvement can be expected.