EPL club in 4-7th place might if they’re desperate enough.
And that’s how you end up at Arsenal
PL clubs don't pay that much.
Everton's highest paid player is at 4m net.
Aston Villa is an odd one since they have Coutinho now but he's at 11m net for half a year. Doubt they sign him fully and doubt they can afford that in the long run. Digne for example is next in line with 5.5m net.
Arsenal's highest earners make 6m net and it's just two of them, the next makes 5m.
Leeds highest earners are at ~2.5m net.
Newcastle got Trippier and they're paying him 5m net. Next in line makes at best 3m.
Tottenham doesn't pay Kane more than 6m net.
West Ham pays like 4.5m net at best.
Even Man City doesn't have more than 4 players making over 7m net.
Man Utd does though and they're a possible destination for Kessié, especially with Pogba leaving. But Kessié is demanding pretty much Pogba money himself (it's 9.5m iirc). Would Manchester United give him that?
The narrative about rich PL clubs ends with their huge transfer fees. They don't pay that much to individuals but their teams gather a lot of players who get overpaid, so a player that gets 1.5m in Serie A will get paid 2.5m there. But they don't have that many 7m net and higher players in that league. They just persuade people that they do
If you discount the two Manchester clubs and Chelsea, everyone else including Liverpool, does not pay that much. Not even their top players.
Liverpool's Van Dijk makes as slightly more than Lautaro these days. And Lautaro would be the 2nd highest earner at Liverpool.
Kessié is demanding more than that!
Salah and Thiago make the equivalent of 6.5m net give or take for example.
You could see a random PL club overpay if it's a household name. But no one knows Kessié over there, they'll devour their management in the idea. If it were someone like De Ligt or Barella I could see it being possible.