Los Colchoneros' boss is hopeful that a deal can be done with both the Spanish outfit and the player himself trying to pish through a transfer.
"Diego is the only player that I have asked the club to sign and I know how hard we are trying to do that," Simeone told AS.
"I also understand the effort Diego is making to come here. We are close and I hope that he will join."
The Brazilian playmaker, whose full name is Diego Ribas de Cunha, played 30 games during a loan spell with Atletico during the 2011-12 season.
Simeone also reflected on his club's search for a new striker that has seen Liverpool's Luis Suarez and Aston Villa star Cristian Benteke linked to the Vicente Calderon.
"We are talking about which characteristics we want, because there are a number of names," he continued.
"I am sure that whoever it is that comes here will be good. We need a striker to fit into the way we play.
"The midfield we could have is strong with Arda, Diego, in all possibility, and Adriuan and we need goals and that is never easy to find.
Diego, meanwhile, has admitted he would like to make the move back to Madrid.
"I know Atletico want me, I would be pleased [to return to the club]," he told Gazeta Esportiva.