The 27-year-old joined Man City from AC Milan last summer for a reported £46.5 million, but after initially impressing, fell down the pecking order.
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Reijnders started just 19 of his 28 Premier League matches, scoring five goals and providing two assists in the process.
According to Marca, Atletico have approached City over a deal for the Dutchman as they prepare for a major summer midfield overhaul.
Atletico have already reached an agreement for Wolves midfielder Joao Gomes, although an official announcement is yet to be made.
It’s understood that City would be open to letting him leave but incoming manager Enzo Maresca is keen on getting a look at him first.r