Pep Guardiola's side tabled a second bid for Sanchez earlier on Thursday after failing with their first £50m attempt.
The accepted offer includes of £55m up front and another £5m in add-ons.
However, any deal for Sanchez hinges on whether the Gunners can finalise a deal for Monaco's Thomas Lemar.
According to Guillem Balague, Arsenal are confident they can sign the winger and have reportedly offered £90m for his services.