Sanchez scored the only goal of the game against Besiktas at the Emirates Stadium on Wednesday to earn Arsenal a 1-0 win that propelled them into the Champions League group phase for the 17th season in succession.
With Wenger revealing afterwards that Giroud could be out for up to four months after undergoing surgery on a broken tibia, it was the ideal moment for Sanchez to showcase his ability to lead the line.
Asked if Sanchez could play at centre-forward during the period of Giroud's absence, Wenger replied: "For three or four months? He can play his whole life at centre-forward.
"I bought him to play striker, not to play only on the flanks."
Sanchez's goal was his first since his £30 million ($50.4 million, 37.6 million euros) move from Barcelona, but Wenger said that he did not see the 25-year-old's strike as the first repayment on his hefty fee.
"I don't see it like that," said the Frenchman.
"He had a good game, not only on the technical side, but on the fighting side. He was mobile, dangerous, and showed as well he has great fighting spirit; qualities that will be very important in the Premier League."
While Wenger admitted that he was "open" to making new signings before the transfer window closes on September 1, he said that buying players was not the solution to the injuries suffered by players such as Giroud and Mikel Arteta.
"If you want to make anybody happy, you just buy all these players," said Wenger, who dismissed links with Manchester United forward Danny Welbeck, Serbian striker Nikola Zigic, and former Arsenal midfielder Alex Song.
"But what's important is the performance on the football pitch and the solidarity we have shown tonight (Wednesday).
"If you look at the players we had on the bench and those who are injured, we have players. You cannot every time buy when a player's injured."
- Bilic draws positives -
Wenger also praised England midfielder Jack Wilshere, who provided the spark of inspiration that led to Sanchez's goal in first-half stoppage time.
"From game to game, he grows," Wenger said. "He got some critics recently and the best response is to show on the pitch that he's getting better and better.
"He has found a little burst back to get away from people, which he hadn't had for a while. In the last two, three games, you see it slowly coming back."
Wenger admitted that Wilshere had been "lucky" not to concede a penalty for sliding in from behind on Ramon Motta when the score was 0-0.
Mathieu Debuchy, who was later sent off for two bookable offences, also escaped sanction after sending Mustafa Pektemek tumbling in the box, but Besiktas coach Slaven Bilic was reluctant to discuss either incident.
The former Croatia coach watched the match from the stands after being sent off in last week's 0-0 draw in Istanbul and when asked to comment, he replied: "You know where I sat tonight.
"You aren't going to be angry if I refuse to answer those questions."
Bilic admitted that the result had left him "gutted", but he said that his side would draw encouragement from their performance over the two legs.
"I'm proud, and we'll come out of this with positives," he told his post-match press conference.
"We're not just in the Europa League to participate. We're going to do business there and we want to go very, very far.
"If we continue to play like this, with a couple more players, we can go far in the Europa League and fight in the Turkish championship, which is always a priority for this club."