Vieira was one of the early frontrunners for the Arsenal job following Arsene Wenger’s decision to leave the club last month.
However, the New York City boss has seen his odds drift in recent weeks.
Another former Gunners captain in Mikel Arteta is the current favourite with the bookies to replace Wenger.
However, Sky Sports claim Arsenal have made contact with Vieira in the last 24 hours.
The report states Vieira is “disappointed” and feels the contact is just a “token gesture”.
Arsenal’s all-time leading goalscorer Thierry Henry, who is currently the assistant manager of the Belgium national team, has not been contacted.
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