Benteke was no more a Rodgers player than he is a Klopp one. He's a more expensive and less controversial Mario Balotelli signing... it makes no sense with the supposed philosophies of the manager of the time.
7 games is hardly a long period in a season. I can understand Mourinho's sacking this season when Chelsea were *that* diabolical and he was getting more and more erratic, but Rodgers' sacking showed they had no faith in him, and that didn't happen overnight.
I think Mourinho, Pellegrini, Pochettino and Klopp are all on top coaches. Pellegrini at United is unlikely because of obvious reasons, but I wouldn't actually mind if he did come here. Unlike Mancini he actually seems like a nice guy... Mancini was an arrogant tosser. I loved Klopp at Borussia Dortmund, and I was disappointed that Liverpool got him.
I do not think that success elsewhere automatically means you will be successful in the BPL though. Van Gaal has undoubtedly had a fantastically successful career, but he has had failures in it before (Netherlands the first time, Barcelona the second time, and arguably Bayern Munich too), and I simply don't think his philosophy is suited to the Premier League. There have been other examples of very successful foreign coaches who've struggled badly in the BPL in the past (Felix Magath, Luiz Felipe Scolari, Juande Ramos... arguably Andre Villas-Boas too). Sometimes it just doesn't work.
If I had to list the top 10 current managers in Europe, I'd probably give the following names:
Pep Guardiola
Jose Mourinho
Carlo Ancelotti
Jurgen Klopp
Max Allegri
Antonio Conte
Diego Simeone
Luis Enrique (easy to argue he's flattered by his players, but he was a good coach before Barca and he's taken them to another level)
Manuel Pellegrini
Mauricio Pochettino
Laurent Blanc might be knocking on the door, but PSG are in such a one-team league that it's hard to really judge him. And Arsene Wenger could be put up there for historical success, but it's hard to really say he is based on recent years.
So, I'd like United to take one of those names, preferably a younger one, and really let them build a philosophy at the club. Fergie was already one of the best rated young manager in Europe when he took over at United thanks to his miraculous exploits at Aberdeen... let's have someone else performing heroics like that.
Going through them:
Guardiola/Klopp/Ancelotti/Enrique are out due to recent changes/realism
Simeone is out because his style of football just isn't compatible with United, despite my great respect for him (I always cheer on Atletico as underdogs there)
Pellegrini is probably out because he's a City manager and I don't think he wants to be hated there.
Mourinho is not a good option, because he is not especially young now, and he isn't the guy to lead you for a generation. I also think he's been quite tainted by two jobs in a row now (Real Madrid and Chelsea). Mourinho 10 years ago would've been a very different prospect.
Allegri did an average job at AC Milan before his miracles at Juventus taking them to the CL final last year, but I don't really think one decent season with an already good club is enough, and I don't think he has much of a playing style.
Conte has been in international management and before that had never managed outside Serie A as far as I know. He'd be quite a risk as a result. However, he probably could be prized away from Italy after Euro '16 this year, so he is an option.
Pochettino performed brilliantly at Southampton, in the PL, and is now performing similarly brilliantly at Tottenham. He's brought through talented young players at both clubs, made them into some of the hardest working and hungriest teams in the league with the highest work rates, and has them playing nice possession football. He's young, he's ambitious, and with some funds behind him, I think he could be magnificent. He should be priority #1 for us to get.
Laurent Blanc has the United connection going for him, but like Conte, he's not managed outside internationals & his national league, and while his job at Bordeaux was very good, his time at France was not. Then again, the French national team is a bit of a poisoned chalice.
So Plan A) Should be Pochettino without doubt. Conte or Blanc are reasonable backups. And Mourinho is a short-term move that just isn't right.