The Gunners boss will meet Sanchez's agent in Brazil this week to convince the forward that he should move to the Londoners ahead of the other clubs competing for his signature.
Liverpool is set to request Sanchez as part of a possible part-exchange deal that could take Luis Suarez to Barcelona, while Manchester United and Juventus also have a strong interest in signing the Chilean.
Arsenal was preparing a bid that matched the Catalan club's 40 million euro valuation of Sanchez after making him its top forward target for this window.
The Gunners have now made their move and are confident the transfer fee and structure of payments they have proposed to Barca will be accepted by the Spanish giants.
Wenger will now attempt to convince Sanchez, whose World Cup ended last Saturday when Chile was eliminated on penalties by Brazil, that he should choose Arsenal ahead of his other suitors.
It was widely reported that a Barcelona delegation was to meet with Liverpool chief executive Ian Ayre in London on Wednesday for an opening round of talks over signing the striker.
Barca president Josep Maria Bartomeu admitted that bids had been tabled from a number of clubs, although he was keen to stress that the Catalunya side is not necessarily going to sell up this summer.
"I can confirm we have received offers from several clubs for Alexis Sanchez," he said at a press conference on Tuesday. "Not just for what he has done at the World Cup but for what he has done before.
"He's a player there in the market that people have got an eye on but he's our player for the moment and he's a basic member of the way our team plays.
"He fits our system, he had a magnificent season last season. He scored a lot of goals, provided assists, had a lot of the ball.
"He's a player we would like to have with us next season. But we are getting a lot of calls from clubs who are making offers to buy Alexis Sanchez."Sanchez, 25, is a player in demand after a series of outstanding World Cup displays and a season in which his 21 goals were bettered at Barcelona only by Lionel Messi.
Arsenal had sent a delegation to Madrid to hold talks with a mystery forward, who is now understood to have been Sanchez.
The Gunners have now stepped up their efforts to sign Sanchez and the seriousness of their pursuit is demonstrated by the fact that both chief executive Ivan Gazidis and contract negotiator Dicky Law were involved in the negotiations in Madrid.
Wenger and his scouts believe Sanchez has the attributes to be developed into a center forward at Emirates Stadium.
The Gunners' top priority this summer is to clinch the signing of an elite forward who can provide competition next season for Olivier Giroud, the only senior striker at Emirates Stadium.
Arsenal tried to sign Julian Draxler in a 30 million pound deal in January and failed with moves for Luis Suarez, Gonzalo Higuain and Wayne Rooney last summer as well as a last-ditch loan bid for Demba Ba.