The Gunners hope to sign the in-demand Chile star ahead of Liverpool, Manchester United and Juventus, with further talks scheduled over the coming days.
The Gunners will now try to wrap up the transfer of the in-demand forward with further talks in the next 48 hours aimed at convincing the player to choose a move to Emirates Stadium ahead of his other suitors.
Sources have told Goal that the financial package offered to Sanchez has been agreed in principle by the player and his representatives.
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Arsenal will attempt to clinch the signing by obtaining an official agreement from the Chile star, with the possibility growing that a deal could be finalized in the coming week.
The indications from the player's camp during negotiations are that he wants to move to Arsenal ahead of Manchester United, Liverpool and Juventus, which have all presented offers.
The timing of the deal could depend upon Barcelona's pursuit of Luis Suarez, with the Catalan club unlikely to formally allow the 25-year-old's departure until it has finalized the signing of the Liverpool forward, who is set to cost just over 88 million euros.
Arsenal manager Arsene Wenger has been busy attempting to convince Sanchez, whose World Cup ended a week ago when Chile was eliminated on penalties by Brazil, that he should choose Arsenal ahead of the rival clubs competing for his signature.
Barca's sporting director Andoni Zubizarreta said Tuesday that the Spanish giants are willing to cash in on the 25-year-old, who has been hotly pursued after a series of outstanding World Cup displays and a season in which his 21 goals were bettered at his club only by Lionel Messi.
Wenger and his scouts believe the forward 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 the club.