Allardyce left his role at the Three Lions last night after just 67 days in charge following a sting operation by the Daily Telegraph.
The Telegraph are now reporting that the FA are set to approach Wenger, who is nearing 20 years at Arsenal, over the vacant role.
And bookmakers BetStars are offering odds of 10/1 for the Frenchman to take the England reigns, despite talk of him signing an extension at the Gunners.
Gareth Southgate, who has agreed to take charge of the England senior side for the next four games, is 1/1 favourite to take the job on a permanent basis.
While Steve Bruce, who is currently out of work after leaving Hull in the summer, is just behind Southgate in the market at 11/5.
GETTY
Arsene Wenger linked with vacant England job
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“Following the remarkable revelations yesterday which led to Sam Allardyce stepping down, market movement has seen Arsene Wenger arrive into the race as an outside bet to take over permanently at 10/1,” said a BetStars spokesman.
“Whilst under-21 boss Southgate has secured the job on an interim basis and is favourite for the full-time role at Evens, followed by Steve Bruce at 11/5, the Gunners’ boss could fit the bill if the FA are prepared to wait until the end of his Arsenal contract.”