The Red Devils are understood to have offered the Chile international a mammoth salary worth more than £500,000 a week to make the switch, on top of paying the Gunners a hefty transfer fee.
Manchester City also showed a strong interest in Sanchez, who they were on the brink of landing in the summer window, only to reportedly pull out due to the escalating costs being bandied about.
Klopp does not believe that money was the key factor in any decision, though, telling reporters: "Now I could really create headlines here, but I won't. It's not my business, not my cup of tea; we had our big transfers and everyone could say whatever they wanted.
"I've nothing to say about the numbers [involved in the deal], but I can't imagine City leave the race because of money. Maybe it's because there are two opportunities in Manchester and maybe he thinks to go to one or the other, and then one maybe thinks, 'I don't want [Sanchez] anymore'. It's not about money.
"Alexis makes sense for pretty much each team in the world because he's a great player. It makes sense, so bring him in whenever. He's a really good player, we are not in for him and that's all I'm interested in."