Wenger is understood to be Madrid presidential candidate Florentino Perez's first choice to become the club's new manager next season should he be elected this summer.
News of Perez's interest coincided with growing frustration amongst Arsenal fans about Wenger's management; the club are without a trophy in four years and some are losing patience with the 59-year-old.
Last week Wenger was involved in a heated exchange at a shareholders meeting where his players were accused of lacking backbone and recent signing Mikael Silvestre was branded ''geriatric''.
On Tuesday chairman Peter Hill-Wood described those comments as ''out of order'' and added that he expected Wenger to at least see out his current contract, which expires in 2011.
Despite previously describing Real's advances as ''strongly interesting'' Wenger is quoted in Wednesday's Daily Mail insisting that he has no plans to quit the Emirates.
''There's nothing to worry about, it's not an issue for me,'' he told the paper. ''I'm staying here. If that changes I will let you know, but don't worry about that. It's not an issue.''