The 28-year old has two years remaining on his contract at the Mercedes Benz Arena, but he fell out of favour towards the end of last season, prompting speculation of an exit.
Kvist joined Stuttgart in 2011 and although he says he is unsure of his future, he acknowledged the attraction of playing in Spain.
"Atletico is a great club and every footballer would like to play in La Liga," the Denmark international told Marca.
"Right now I am at Stuttgart, but I don't know what will happen. In case I was close to a move to Atletico, I would not tell anyone."