The Blues forward wants to rejoin Diego Simeone's side having been frozen out at Stamford Bridge, with Costa yet to have returned to the club since the conclusion of the 2016-17 season.
Costa revealed that he had been told by manager Antonio Conte that he was surplus to requirements but now claims the Blues are demanding too much money for him to be able to leave.
He told ESPN Brasil: "I've demonstrated I care for Atletico and have interest in playing for them.
"But if Atletico and Chelsea don't come to an agreement and Atletico don't make a big effort, I can't keep on wanting to play for a club that isn't going to make a bigger effort to try and sign me.
"I know that this [big effort] will happen, but if it's to pay the amount that Chelsea want it won't be possible.
"What I know is that this offer Chelsea will get is bigger than what they paid [when they signed Costa from Atletico for £32 million in July 2014], so I've given them something back in all senses.
"I don't know [how much Chelsea want for him], but my agent said that Chelsea want something that Atletico can't get near.
"When we heard that Conte didn't want me anymore, my agent went to find out if there was interest from Atletico for me coming back.
"Of course for the warmth and respect that I earned there, they showed interest. But they wouldn't pay a fortune. Atletico is a team growing every year, a big team, but they can't pay an extraordinary amount."