Wenger is keen to add more stability to his midfield with Jack Wilshere in need of rest and the likes of Abou Diaby and Mikel Arteta constantly struggling with injuries.
Gourcuff has failed to rediscover his younger form since he joined Lyon in 2010 and the French club are happy to allow the midfielder to leave on loan if the price is right.
Arsenal and Atletico would both be interested in a loan deal until the end of the season with a view to a permanent switch if he impresses.
La Liga club Atletico have already spoken with Lyon about the possibility of a loan but club agent Nikola Franco has revealed that a loan fee of in the region of £2.5million would be out of the question if a deal was to happen this month.
“Atletico are interested in Yoann Gourcuff,” he told 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.”