Agent, Jonathan Hope, who is working on securing the UK mandate for Benzema, has revealed he has put forward the player as a possible arrival at the Etihad Stadium this summer.
"I have put Benzema forward after a talk with a very reliable and high source at Manchester City as a possible summer signing," Hope told Sky Sports.
"We are working closely to secure the exclusive mandate to obtain the paperwork firstly after a serious interest from the champions.
"We spoke with Manchester United two years ago and it went nowhere, which I can see is perhaps a regret on their part.
"The player has stated himself he will not go to Manchester United, however, he has not ruled out a switch to join the champions. I will have a clearer picture soon after the Euros when I have time to sit with his representatives.
"But personally I can see the business being done and to be fair it will rock English football.
"I must stress this is at discussion stages. All does seem in good order but this is football and things change fast."