The 22-year-old midfielder, who has made 160 league appearances for the Gunners since arriving in 2003, has long been linked with a big-money move to former club Barcelona, as well as fellow la Liga giants Real Madrid.
However, according to a recent Tuttosport report, it is the Rossoneri - with Kaka having moved to Madrid and fellow midfielder Andrea Pirlo being tipped to join Chelsea - who were thought to be set to launch a €35 million swoop.
The report suggested that Milan vice president Adriano Galliani had an agreement in place with owner Silvio Berlusconi to move for the Spanish international, with the San Siro giants believed to be ready to offer Fabregas €4 million-per-season to leave North London for Italian shores.
However, Emirates Stadium chief Hill-Wood has now insisted that their skipper will be going nowhere.
"There is absolutely no chance of us selling Cesc and all this talk is just fabrication," he said.
"This sort of thing crops up from time to time and it is something we are perfectly used to.
"Cesc is happy at Arsenal, as far as I am aware."
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