The former Arsenal captain, who made 406 appearances for the Gunners during a nine-year spell in north London, has been touted as a possible successor to Arsene Wenger, who stepped down from his role at the end of the season after 22 years in charge.
Two former club captains Mikel Arteta and Vieira, now head coach at New York City in the Major Soccer League, are among the favourites for the role.
The Gunners had initially planned to name a new manager before the World Cup, but the announcement could now come earlier than scheduled, with Arteta set to make his first strides into management.
It is understood the new manager will be able to bring in his own backroom staff.
Mikel Arteta given Arsene Wenger backing for Arsenal job
'He is doing very well with New York City, and he told me the job is very hard and difficult.
Arteta meanwhile has reached the point in his negotiations with Arsenal where he has "named potential staff and the financial package required", and among the people he wants working with him is Santi Cazorla.
Arsene Wenger has reiterated he will not take another job in the Premier League as it would feel like a betrayal of Arsenal.
Iran's Rouhani slams some Arab states for "silence" over killings of Palestinians
Rouhani finally said some assume that pressure, sanctions and military threats can force the Iranian nation to surrender. He said that it is the United States, rather than Iran, that needs to be accused of wrongdoing.