While praising Giroud's role in France's World Cup triumph in 2018, Benzema was disparaging of the veteran when asked to compare themselves.
The Real ace said it would be like comparing "a F1 with a go-kart".
A widely reported response from Giroud, claimed he said: "I will be a kart, but with a World Cup..."
But BeFoot says the quote comes from them - and was an April Fool's joke.
They posted to social media: "Good guys .. Did you see the date today? We are April 1, so of course this statement is a fake? (Quiet Karim it was a little joke, and Olivier please do not attack us in court)."