The Gunners comfortably beat Rangers 3-0 on Sunday to lift the Emirates Cup, with Jack Wilshire netting twice.
Though Eduardo and Tomas Rosicky are both fit to feature in the opening matches of the Premier League campaign, Samir Nasi has been ruled out for three months with a broken leg.
And with a £30m transfer kitty ready to be utilised, Wenger says he will spend this week finalising his squad, and mulling over a move for Vieira.
"Patrick is a great player. I have not considered it yet to bring him back, but it is a possibility I have to think about,'' he said.
"First of all, it is not sure he will decide to join us if I decide try to make him come. There are a lot of thoughts to be done.''
Arsenal have been linked with 22-year-old St Etienne midfielder Blaise Mutuidi, as well as Bordeaux's Moroccan striker Marouane Chamakh and Real Madrid forward Klaas-Jan Huntelaar. Wenger, though, prefers to do his negotiations in private.
"We don't make any comment about the transfers. If we sign someone we will come out with it,'' he said.
"I read in the newspapers that I have called him and called him, I go for so much, but I never speak about that because you have to accept that it might disturb the player, it might disturb the club.
"If transfers don't happen you have an unhappy player, so I keep it as quiet as possible.''
One player who certainly is set to feature for the Gunners next season is 17-year-old Wilshere.
With national team manager Fabio Capello at Emirates Stadium on Sunday and English football about to embark on a campaign which will hopefully end at the 2010 World Cup finals, attention is bound to be extra focussed on the potential of any home-grown talent.
Wilshere is already an England youth international, and won the FA Youth Cup with Arsenal last season, having broken the club's record for their youngest player to appear in the first team.
Wenger, though, urged on the side of caution to allow the Hertfordshire-born midfielder the required time to develop.
"I sped him up by putting him in the dressing room and giving him a chance to practice every day with the first team,'' said Wenger.
"If I had taken him out of the youth team now, you would not have seen what we did today, that means he has benefited a lot from special treatment and an acceleration of his education.''
Wenger admitted: "I do not know how much he will play. It is very difficult to predict. The only problem in England, knowing the impatience of English people, is that it will be difficult to keep the right pace in his progress.
"Let's be calm and quiet. There is still a year to go to the World Cup, and let's see how he improves, how he is consistent. Let's not make stars in just two games. You have to respect the development of the players.''
Meanwhile, France international Nasri has spoken of his relief that his leg injury occurred in the middle of the Gunners' pre-season preparations rather than during the forthcoming campaign.
The 22-year-old told French sports daily L'Equipe: "I am happy that it is only a simple fracture of the fibula.
"It is better to happen now rather than right in the middle of the season. Now I just have to be patient. I have about three weeks of immobility before starting my rehabilitation at the start of September.''