Real are targeting several players as new manager Jose Mourinho looks to build a squad capable of adding silverware to their trophy cabinet.
Los Merengues have already added Argentina winger Angel di Maria to their ranks, while Gerrard and Cole are thought to be on Mourinho's wish-list.
Chelsea defender Cole played under the Portuguese at Chelsea, while Mourinho is known to be a long-term admirer of Liverpool captain Gerrard.
Ramos believes the pair will make the switch to Spain an is especially hopeful on Cole.
He told the Daily Star: "We are a club that is always looking to improve by adding the best players in the world.
"We have a proven record of signing English players - with David (Beckham) and Michael (Owen) - and it would not surprise me at all if our two new arrivals this summer were English. Ashley Cole is a terrific player.
"For me, he is by far the best left-back in the world and, along with (Didier) Drogba, Chelsea's best player.
"I am sure Chelsea will do all they can to keep him but he had a difficult year in England.
"A change might be what he is looking for. When a player is the best in his position in the world and doesn't play for Real Madrid, you have to consider it a waste.
"He has done everything in England for Arsenal and Chelsea. It's now time for him to come and win La Liga and the Champions League with Real Madrid and Jose Mourinho.
"Jose will know all about him. He has a history of signing players and trying to sign players from his previous clubs. More importantly, players seem to love playing under him.
"I spoke with Cristiano Ronaldo about him - and he told me Cole is the toughest defender he has ever played against.
"That's quite a compliment coming from the world's best player and he is exactly the sort of player we want."
On Gerrard, Ramos added: "I think Madrid's admiration of Steven Gerrard is not a secret.
"He is at the point now where he needs to win things. I can guarantee that under this Real Madrid set-up he will win things.
"I really think both of them are Real Madrid-bound."