Costa has had two spells at Atletico already and was particularly successful between 2012 and 2014 under Diego Simeone, helping the Madrid team to La Liga and also the Champions League final before a move to Stamford Bridge.
The Brazil-born forward, who now represents Spain at international level, has won two Premier League titles in his three seasons at Chelsea, but recently revealed he had been told by Blues boss Antonio Conte that he is not in the Italian's plans for the 2017-18 season.
Atletico are interested in bringing back their former forward, but failure to overturn their transfer ban for irregularities in the signing of young players means he would be unable to turn out for the Rojiblancos until January.
"It's a difficult situation," Kiko told Goal. "I understand the player. He can't be sat out for five months in a World Cup year. He needs to play. The player wants to come, but the transfer ban makes it complicated."
Chelsea want the 28-year-old out of the club and believe he may be a disruptive influence if he stays, while FIFA rules mean Atletico would not be able to send the player out on loan due to their ban.
However, Atletico could convince Chelsea to loan out the forward for six months and then sell him to Atletico in the winter window, a solution that would appear to suit all parties.
"Let's hope he can come back," said Kiko, who was speaking at the LaLiga promises event in New Jersey. "Because he is the ideal centre-forward for Atletico and for Simeone's style of play.
"He has all the right characteristics: he has the character, that contagious enthusiasm about him, he presses high up the pitch, he can play on the counter, help control the ball, hold it up and he never stops working. He puts himself at the service of the team."
While Costa could arrive, Antoine Griezmann has announced he is staying at the club and Kiko believes that is a big boost for Simeone's side ahead of the 2017-18 season.
"He is among the five to eight best players in the world," he said. "He is another one who works hard for his team-mates and that is hard to find in football these days. He's a top player."