The Juventus boss was quizzed on his future following his side’s 1-1 draw away to Udinese.
Express Sport understands the Italian has been locked in talks with the Gunners since the end of 2016.
And it is believed Allegri is now waiting for Wenger to decide over his position at Arsenal, with a two-year extension still on the table.
While Arsenal chiefs await their manager’s verdict, Allegri has endured problems at the Serie A giants, having fallen out with a number of senior players.
But he has insisted no such agreement with the Gunners has been reached yet.
“The rumours from England are not true,” Allegri said.
Who is Massimiliano Allegri?
Sun, February 7, 2016Express Sport takes a look at Chelsea manager target Massimiliano Allegri's career in pictures
Who is Massimiliano Allegri?
Juventus would be the first to know
Max Allegri
“And I’m not the one to decide my future – Juventus will.
“And if these rumours were true, Juventus would be the first to know and I haven’t talked to Juventus yet.”
Arsenal want to know whether Wenger is signing on beyond this season by the end of March.