The talented but inconsistent Gourcuff, 26, has had a stop-start time at Lyon since joining from Bordeaux in 2010.
A combination of injuries and a loss of confidence have seen him lose his place in the national team, but a recent improvement – combined with Lyon’s desire to reduce the wage bill – mean a transfer to La Liga could be on.
“Atletico are actually interested in Yoann,” agent Nikola Franco, who is known to tout his clients to other clubs, told L’Equipe.
“But the club will not pay a fee to loan Yoann – they want a free loan with the option to buy at the end of the season.”
Lyon are understood to want money up front for Gourcuff as they seek to offset the cost of a new stadium.