The France international has been a long-term target for Gunners boss Arsene Wenger, but Wenger faces competition for his signature from the La Liga title contenders.
Gourcuff first attracted attention when his performances proved pivotal as Bordeaux won the Ligue 1 title in 2009, but the Frenchman opted to move to Lyon rather than abroad.
A difficult couple of years at Lyon has prompted speculation Gourcuff could leave the club this month, with Arsenal and Atletico Madrid thought to be keen to sign him, initially on a loan deal.
And Nikola Franco, an agent working with Atletico Madrid, has revealed Diego Simeone's side are exploring the possibility of bringing Gourcuff to the Vicente Calderon.
"Atletico are interested in Yoann Gourcuff," Franco told French newspaper L'Equipe. "But the club does not want to discuss a loan fee with Lyon. The only option proposed by Atletico is a free loan with a purchase option at the end of the season."
Lyon are thought to be willing to let Gourcuff leave on loan - but only for a fee of £2.5m.
The 26-year-old has 29 France caps, but was expected to become one of his country's most important stars when he first broke into the Rennes team aged 17 in 2003.
His time at Rennes provided the platform for a move to AC Milan, but the attacking midfielder never settled at the San Siro, eventually returning to France three years later on loan.
Having signed for Bordeaux, Gourcuff quickly established himself as the team's creative heartbeat, and convinced the club to fork out €13.6m to sign him on a permanent basis a few months later.
But he only spent a season and a half with Bordeaux, before Lyon spent €22m to bring him to the Stade de Gerland - but Gourcuff now looks like he could be on the move again.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms