The Gunners are hoping to add to their frontline to secure the Premier League title.
The Sun states that Arsenal have made a £22 million bid to sign Mayoral immediately.
The club are hoping that they can strike a compromise with Getafe, who want considerably more money.
The Spanish club are willing to sell Mayoral, but only for a fee in the region of £39 million.
Mayoral, who is now 26, has scored 12 league goals for Getafe so far this season.