The Red Devils are down in eighth in the Premier League having lost three of their first eight games of the season.
Mourinhos side were also knocked out of the Carabao Cup last month by Championship club Derby County.
It has been a different story at the Emirates, however, with the Gunners winning nine consecutive games to climb to third in the top-flight.
And former Arsenal striker Wright believes the turmoil at Old Trafford has helped his former club and Arsene Wengers successor.
Arsenal fans have not had too much to thank Jose Mourinho for over the years. But for once, they have every reason to be giving the thumbs up to the United boss, he told The Sun.
And while they are at it, Manchester City chief Pep Guardiola and Jurgen Klopp at Liverpool have done the Gunners a bit of a favour as well.
OK, it has hardly been through choice – certainly in the case of Portuguese Mourinho.
But between them, those three allowed Unai Emery to stay in the shadows for the start of his Arsenal reign.
All the spotlight for the past month has been on Mourinho. Before that it was very much on how Guardiola and Klopp were going to battle it out for the Premier League title.
And that meant Emery could largely get on with it at the Emirates without the glare of the spotlight on his every move.
Arsenal suffered consecutive defeats at the start of the season – losing to Manchester City and Chelsea.
But they have since put together a hugely impressive run and Wright believes Emery deserves full credit for the job he is doing in north London.
Dont let anyone talk down what Spaniard Emery has achieved over the past couple of months at the Emirates, former England international Wright added.
Im not getting carried away and suggesting all of a sudden Arsenal are champions in waiting.
But I am certainly enjoying the ride at the moment – and every Gunners supporter should be doing the same.
Look, not being under the microscope might not have made the slightest difference to how things have gone but it has certainly not done any harm.
What Unai is doing is trying to change the whole philosophy going forward, and he is doing it very, very well indeed.