I have seen so many silly top 10s on the Internet regarding this topic, including one made with AI, and some of them are absolutely ridiculous, putting even PSG or City over teams like Milan and Inter for example.
There are nine clubs that are sacred for the sport and should not ever be left out of any historic top 10, regardless of the order in which you put them and those are Real Madrid, Barcelona, Bayern Munich, Liverpool, AC Milan, Manchester United, Juventus, Inter Milan and Ajax. And no other team in Europe(and frankly, the world), is bigger than any of them.
After those 9, put whatever club you want, put a Portuguese one, or Arsenal, or Chelsea, or whatever. But those 9 are non negotiable and leaving them out honestly makes any top 10 look either ignorant or made by a really young person.
Edit: And I mean big as in overall trophies, status, prestige, players, ballon d ors, history, fans, etc. Not just followers on social media and revenue.
Arsenal fall into a weird spot where they are ahead of clubs like Chelsea, Forest, City in terms of long term domestic history and domestic cultural relevance, but simply fall short on the European stage behind clubs like Inter and Benfica who many in the UK would see as less relevant, let alone City and Chelsea.
Arsenal are tied to a revolution in the professional game through Wenger in England, and I think even one, or two CL victories would immediately plant them amongst those European giants.
As it is, they just fall short