The club are keen to return to the Champions League after a four-year absence.
The Frenchman has been heavily linked with the post amid speculation that high-ranking officials at the club are becoming exhausted with the lack of progress made under Gennaro Gattuso after a £130million summer spending spree.
And chiefs Paul and Gordon Singer, who support Arsenal, are keen to get Wenger on board.
"The only thing I can say is that it's fake news", Wenger said while on beIN Sports.
" If I signed somewhere I would tell you but that is wrong news". While the 69-year-old French global has been linked with the vacant seat at Real Madrid in the last week, emerging reports indicate he will moving to Italy to take charge of AC Milan.
"I believe I will start again on 1 January", Wenger recently told SportBILD.
The Frenchman has not worked in football since stepping down as coach of the Gunners at the end of last season after 22 years at the helm. "At the moment I'm having a good rest and I watch football a lot".
A host of big clubs are rumoured to have approached Wenger, with Bayern Munich and Real Madrid considering hiring a new manager.
Life after Wenger at the Emirates Stadium has not been as bad as first feared.
Current boss Gennaro Gattuso is on the verge of being shown the exit doors despite claiming six win in his last eight matches.