The Gunners are reportedly willing to make him the second biggest earner at the club.
The Gunners `are keen to add a striker to their squad this summer after Olivier Giroud and Theo Walcott struggled for consistency last season.
They have already seen a move for Jamie Vardy fall through after he opted to stay with champions Leicester City when Arsenal activated a release clause in his contract.
One man they have been linked to is striker Alvaro Morata, who looks set to leave the Bernabeu this summer.
Real opted to activate a return clause in his deal at Juventus, but are reportedly looking to sell him on for a quick profit.
According to AS, Arsenal are one of those that are interested in his services and are willing to give him huge wages to ensure he makes the move to the Emirates Stadium during this transfer window.
The Spanish publication reports they have already offered him £7.5 million per year, which works out at around £156,000-per-week.
That sort of price would make him the second highest earner at the club should it be true, with Mesut Ozil currently earning around £190,000-per-week according to the Daily Star.