Costa was Chelsea's top scorer as they lifted the Premier League title last season but reportedly clashed with Antonio Conte amid mid-season interest from Chinese Super League side Tianjin Quanjian.
The Italian has told Costa he is surplus to requirements at Stamford Bridge and, as expected, he was absent when Chelsea lost to Arsenal on penalties in the Community Shield at Wembley on Sunday.
The 28-year-old striker has expressed a desire to return to Atletico, although the fact his former club are under a FIFA player registration ban until January complicates matters.
Atleti forced through a controversial move for Sevilla winger Vitolo, who will spend the first half of the season on loan at Las Palmas, but Simeone seemed reluctant to entertain making similar allowances for Costa when addressing the media after a 3-2 friendly win at Brighton and Hove Albion.
"I don't want to comment too much," he said.
"The fact is he is still with Chelsea.
"The most important thing to me is the work of my club in general, not only in training. I have to work with what I have.
"When I found there was no other possibility to get new players at the club I accepted it.
"Maybe I could improve the quality, but for the moment with this team I can work very well and I'm satisfied with that."
This week, Costa's lawyer Ricardo Cardoso underlined his client's stance that he only desires a move to Atletico when stating the Spain international will submit a formal transfer request at Stamford Bridge.
Chelsea insist Costa has been aware of their position on his future since January this year, while AC Milan sporting director Marco Fassone has held talks with the player's agent Jorge Mendes.