Vieira said Arsenal have not contacted him about replacing Arsene Wenger but the former Gunners captain has not ruled out a return to the club.
The 41-year-old Frenchman has said it would be “difficult” to leave New York City but his contract at the MLS side expires later this year.
Carlo Ancelotti, Mikel Arteta and Luis Enrique are the leading candidates to take over from Wenger but Vieira has confirmed he is open to a dream return to Arsenal.
Vieira said: “Of course it is an honour to be mentioned with Arsenal. It was somewhere I spent nine years and I love the club. I played my best football there and made my name in the game. I am always going to have a deeper relationship with Arsenal.
“That [alone] is not enough to coach that team but I am ready to coach any side in Europe.
“I do not want this to be perceived that I want to go, because I do not want to leave. But if the question is as simple as, ‘are you ready to manage any teams in Europe?’ then I would say, ‘yes. I am ready’.”
Arsenal have started the search for Wenger’s replacement following last Friday announcement that he will leave at the end of the season.
Chief executive Ivan Gazidis, along with head of football relations Raul Sanllehi and head of recruitment Sven Mislintat, have begun to draw up a shortlist of possible candidates. Arsenal could also look to bring in a former player to form part of a new coaching set-up and Vieira told The Times: “I think we are all doing this job because one day we want to coach the biggest teams in Europe. Just like when you’re a player, you want to play for the biggest clubs.”
Meanwhile, Jack Wilshere is fit to face Atletico Madrid on Thursday in a major boost for Arsenal ahead of the first leg of their Europa League semi-final.
The midfielder missed Sunday’s 4-1 win over West Ham in the Premier League with an ankle problem but trained with team-mates this morning.
Mesut Ozil will return after flu but Henrikh Mkhitaryan has not recovered from his knee injury. Wenger hopes the Armenian will be fit for the second leg in Madrid next week.
The manager faces a difficult decision over whether to play Petr Cech or David Ospina. Cech was in goal for both legs of the previous round against CSKA Moscow and has said he wants to play despite Ospina being told he would feature in cup competitions when fit.
Arsenal could face Diego Costa Thursday night after the former Chelsea striker was included in Atletico’s squad following two weeks out with a hamstring injury.
Atletico manager Diego Simeone confirmed Costa was travelling to London but had previously indicated the Spain striker was unlikely to feature in the first leg.
The 29-year-old looks certain to be fit for the return and Arsenal will hope he is not their undoing as they bid to give Wenger the perfect send off after 22 years in charge of the club.