The Japanese midfielder is free to speak to interested clubs about a Bosman deal given that his contract is due to expire on 31st December.
Even if a number of top European sides have been showing interest in Honda, Sevilla and AC Milan were the first to submit official proposals.
Due to huge financial problems, los Rojiblancos cannot compete with other top sides, but they are still hoping to persuade the Japan international to join them in the winter.
Sevilla had tried to sign Honda some three years back, but he ultimately joined CSKA in a big money move from VVV Venlo.
Keisuke Honda, 26, has proved his worth in Russian Premier League, scoring 19 goals in 76 league matches, but he is now set to test his skills at the biggest stage as he hopes to join a top European club.