The French defender was handed the armband for Wednesday night's 1-0 defeat by Salzburg in the final match of the Gunners' pre-season trip to Austria.
Wenger maintains there is "no problem" between him and Gallas, who turns 30 next month, despite the harsh criticism of the club from the former Chelsea man over the summer.
Gallas had claimed "several players are questioning the club's future" following the departure of talisman Thierry Henry to Barcelona and that he was "not at Arsenal to play for third place".
The Gunners boss, however, shrugged off suggestions there was any rift with the World Cup finalist, who had an injured-plagued season last year, and indicated Gallas was one of the leading contenders to take over from Henry as first-team skipper.
"William has all the ingredients to be captain - it is him or [players like] Gilberto, Kolo [Toure]," said Wenger,
"He has got a lot of experience. At the back is the best position to captain the team because you are in a position where you see all the problems on the pitch - that is a better position than for a centre-forward or wide player."
Brazil midfielder Gilberto stood in for Henry during last season, but is not set to link up with the Arsenal team until early August following a break after the Copa America.
Wenger, though, maintains the decision on who will lead his side out at Emirates Stadium for the opening game of the new Premier League campaign against Fulham on August 12 is not high on his current agenda.
"We go game by game," he said in an interview broadcast by Arsenal TV Online.
"We are in a preparation period at the moment and at this time, the captain problem is not the most important problem for us - it is to be fit.
"You have to give us some time, show patience and continue to play with the spirit we have shown in Austria."
Despite the loss at Bulls Arena on Wednesday, Wenger was content enough with the performance of what was a strong side.
New signing Eduardo da Silva made his first start, and could have put the game beyond the hosts before Vladimir Janocko eventually hit a 76th-minute winner.
"He has worked very hard and has shown he has top quality," said Wenger of the Brazilian-born Croatian striker. "He could have scored four."
Wenger added: "Apart from the result, everything else was okay.
"We faced a team who played very deep and defensive, which is a situation we face in our league.
"We created some chances and things we had worked on went well.
"Of course, we are not sharp at the moment, but overall what we wanted to see, we have done - the intensity of the workout was there."
Wenger reported winger Tomas Rosicky had been taken off as a precaution with a tight hamstring, but is not expected to be a major concern.
The Arsenal boss, meanwhile, revealed the departure of veteran midfielder Freddie Ljungberg to West Ham earlier this week did "not necessarily" mean he would be making another move in the transfer market.
Wenger will continue his squad's preparations for the new campaign with the Emirates Cup this weekend, which will also feature Inter Milan, Paris St Germain and Valencia.
Arsenal are scheduled to take part in the Amsterdam Tournament next week before focus turns to the visit of Fulham, which will be swiftly followed by the first leg of their Champions League third-round qualifier.