The Brazilian-born Spain striker faces a potential three-game ban after he appeared to tread down on the 21-year-old German early in the first half of their League Cup semi-final, second leg at Stamford Bridge on Tuesday.
Should he fail in his challenge he would miss Saturday's top-of-the-table clash against Manchester City as well as games at Aston Villa and home to Everton.
Costa was later involved in a second stamping furore involving Liverpool's Slovakian defender Martin Skrtel, but the FA said they would not take any action over that incident.
Chelsea reached the League Cup final thanks to a towering header from Branislav Ivanovic in extra time to give them a 1-0 victory on the night and 2-1 aggregate success.
Chelsea, who cancelled their usual pre-match news conference ahead of the City game, are five points clear at the top of the table.
(Reporting by Toby Davis, editing by Pritha Sarkar)
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