The 24-year-old is regarded as one of the best wingers in European football and has long been linked with a move to Manchester United.
However, according to former Brazilian defender Carlos, the Russian club have moved to the head of the queue.
"There were already talks in the summer but various agents appeared so we backed out. But now we are expecting a good solution for all parties," he told O Jogo.
Gaitan has six Argentinean caps to his name.