Manchester United should better do away with ten hag, they should shop for a new manager and stop managing a bad situation. Allowing Ten hag to manage Manchester United for the next, is like allowing a bad situation to get worse, he doesn't have the tactical firepower to turn things around for an elite club like United, a manager that couldn't manage an asset like Ronaldo has a long way to go.
As for Rashford, if PSG is coming for him, then he should go, let him try something new on a different ground, he has afforded a wonderful contribution for Manchester United over the years, but given his long stay and the aura within the club at the moment, i don't think he will be offering anything super new to the club because we've seen the best he can offer.
Manchester United management may not have found a better and more qualified manager than Ten Hag, so they decided to keep him next season. There are also other considerations, Manchester United will have to pay compensation if they fire Ten Hag, it could be that they are reluctant to do so. In my opinion, there are many other factors why Manchester United management is still retaining him, what is clear is that Ten Hag is considered still eligible after evaluation. Besides that, Rashford will most likely not be released to PSG, he is an important player in Ten Hag plans next season. PSG wants to recruit Rashford as a replacement for Mbappe, but it is very likely that their plans will fail to materialize. Joining PSG is actually not a bad move, because there Rashford will be able to taste trophies every season.