The winger is one of the Lyon players expected to leave the Ligue 1 club this transfer window, with Lisandro Lopez, Michel Bastos and Bafetimbi Gomis also believed to be departing.
Aulas said that Briand, the French club and the Istanbul-based team must agree on a deal before anything is official, but admitted a bid had been made and talks are in progress.
"We accepted a proposal from Besiktas," he told BeIn Sport.
"But, before any transfer or a loan can be realised, it is essential that all three parties are in agreement. This is not yet the case."
Briand has made 10 appearances for Lyon in Ligue 1 this season having struggled with injury, scoring once in the process.