The Real Madrid forward is considered to be one of the most complete forwards on the planet.
In the past Manchester United, Chelsea and Arsenal have all expressed interest, but it is the latter team that maintain a strong desire to bring him to England.
Benzema isn't everyone's cup of tea at the Bernabeu despite being a prolific goalscorer and, with the sale of Mesut Ozil, Madrid have proved they are willing to sell big names in order to recoup the money spent on Gareth Bale.
With Giroud their only viable first-team striker, Benzema may be ideally suited to a big-money move from Arsenal in January. That's if there isn't others that get there first should he find himself unhappy in the Spanish capital.