Wenger is on the Football Association's hit list to replace Roy Hodgson following England's woeful Euro 2016 showing.
Hodgson quit following his team's abject 2-1 defeat against Iceland on Monday and Wenger has been mooted as a possible replacement.
The Frenchman's existing Arsenal deal still has a year to run.
But there is hope within the FA that Wenger could be coaxed into international management.
However, The Sun suggest bigwigs in north London do not want Wenger to leave the club at all.
It's suggested they are preparing to offer him a new two-year deal to remain at the Premier League giants.
And Arsenal are reportedly confident he will not have his head turned by the England job.
