However, Vieira revealed that talks with Arsenal were brief and did not go any further than an initial conversation as the club instead looked at other targets.
"Their executives met through a process which included a conversation with me but it didn't go any further," Vieira told The Times.
"I have been allowed to grow as a coach and gain valuable experience. That has helped me become much more clear in my approach, my vision of football.
"A game is there to be won. I want to enjoy myself on the bench, to have a team play football I want to see. To be bold."
Vieira made more than 400 appearances for Arsenal between 1996 and 2005, leading the club to three Premier League titles and three FA Cups.