After Arsene Wenger announced he was leaving the Gunners this summer, Vieira was quickly installed as one of the favourites to replace him.
Arsenal CEO Ivan Gazidis had promised that the club will be "bold" in their search for Wenger's replacement after 22 years in charge.
Arteta is a former Arsenal captain who played for the club from 2011 to 2016.
Another candidate was Hoffenheim's Julian Nagelsmann, but the German club recently insisted he will still be their manager next season.
That leaves Arteta in the clear as it has seemed for some time that Arsenal wanted a younger coach with fresh ideas to reinvigorate their squad after a disappointing past two seasons under Wenger.
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Arsenal's managerial target Mikel Arteta will offer veteran midfielder Santi Cazorla the chance to join his backroom staff if Manchester City's assistant coach is offered the main role in north London this summer.
Is Arteta a good fit?
Juventus boss Massimiliano Allegri remains most fans' first choice to replace Wenger, despite appearing to indicate his desire to honour the final year of his contract after securing a fourth straight league and cup double last weekend.
Patrick Vieira is understood to have viewed his approach as a 'token gesture', and The Telegraph reports that Arsenal are now planning to accelerate Arteta's appointment after the Spaniard was left as their only serious candidate.
Arteta has come out of left-field a little, especially with no prior managerial experience, but in many regards he would be the ideal choice to not only replace Wenger but keep the playing style and culture he cultivated intact.
Yates extends Giro lead with 11th stage win, Froome slips further
He is one of just two British riders with more than one stage win in the same Giro, the other being Mark Cavendish. Four children and five adults were pulled alive from the snow and debris days after the avalanche.