The Premier League leaders nearly signed him at the start of the season before Arsenal pulled the plug at the last minute, though reports continued to suggest they had been in talks to sign the forward, whose contract expires at the end of the season.
But United came in under the radar and met Arsenal's demands in the shape of Mkhitaryan, while the saga prompted some suggestions Sanchez has chosen United over City because of the money on offer.
Klopp suspects that to be nonsense, however, while also acknowledging that Sanchez "makes sense" for any club in the world.
"Now I could really create headlines here, but I won't," Klopp said with a smile when asked about the Chile international at his news conference on Friday.
"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 him [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."
As for Klopp's own transfer dealings, the German is not expecting much movement from Liverpool in January, despite the sale of Philippe Coutinho.
"If something [an opportunity] jumps in my face, then maybe we think, but we aren't looking actively at players we don't already know, like that would be a solution," Klopp said.
"We have to use the high quality players we have and I think that makes sense because we have quality players.
"[Adam] Lallana isn't a replacement for Coutinho, but he's fantastic and is back. He couldn't play in [the second half of] 2017, but no he's back and that's good. But I couldn't say we're active [in the transfer market]."