Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The France striker had been linked with a transfer to the Emirates Stadium, with Arsenal manager Arsene Wenger determined to strength his squad significantly before the September 2 deadline.
However, agent Karim Djaziri has told French newspaper Le Journal du Dimanche it is a deal that will not happen.
Djaziri said: "We can't stop the rumours. But I tell you: Karim will not go to Arsenal. It's never been a question for him and no contact has been made.
"He will stay at Madrid. The probable arrival of Gareth Bale at Real Madrid doesn't threaten him at all. Cristiano Ronaldo and Bale will play on the wings and Karim in the centre."
Benzema is contracted to Madrid until 2015 and Djaziri said talks are ongoing over an extension, saying: "Karim could very well finish his career at Real, the club of his dreams."