In three seasons at Chelsea, the 28-year-old has collected two Premier League crowns and a League Cup while netting 58 goals in 119 outings.
Despite his success in England, a big-money transfer has been mooted when the window re-opens, with Atletico open to the idea of welcoming the burly frontman back into their fold.
Saul told AS: "If he can be signed, if he comes, Diego Costa would be well received.
"He knows the place, we know him, and he would not take long to fit into the play of Atletico Madrid.”
Saul believes Costa could be “happy” back in the Spanish capital, with Koke’s commitment to the club proving that there is no need to leave in order to be successful and content.
He added: "Fernando Torres, Gabi, Koke show the values of Atletico Madrid, a family club, humble, hard-working.
"Koke could have earned much more money [at another club] but he prefers to be happy. When you are wearing the jersey that you love, and are getting playing time, in the end you value that much more than other things."
While keeping a close eye on Costa’s situation, Atletico have also been linked with Lyon striker Alexandre Griezmann as they fight to keep talismanic forward Antoine Griezmann at the club.