Gunners are one of 11 clubs, including Manchester United and Internazionale, who are interested in recruiting Real Madrid supersub.
The Spaniard, a local Madrid kid who has represented Atletico Madrid, Getafe and has been with Real since progressing out of their youth set-up in 2010, has received limited pitch-time under the stewardship of Carlo Ancelotti - largely because of the wealth of experienced attackers ahead of him, like Cristiano Ronaldo, Gareth Bale and Karim Benzema.
Los Blancos may even supplement their striking ranks should they succeed in attempts to purchase either Sergio Aguero of Manchester City or Liverpool's prized possession Luis Suarez.
Morata competed in 23 La Liga outings last term, yet the vast majority of those were as an impact substitution, so he only played 578 minutes worth of league football.
However, despite that, he showed an ability to make his chances count as he created a goal-scoring opporutnity every 41 minutes, attempted a shot on goal every 14 minutes and scored every 72 minutes - statistics that are far superior to Premier League strikers such as Javier Hernandez, Alvaro Negredo and Romelu Lukaku.
It is no wonder Morata has attracted foreign interest.
British media reports had speculated that Arsenal were embroiled in a two horse race for Morata's signature, should the wonderkid be made available in the summer market, as the Daily Mirror linked the Gunners with the player on numerous occasions while The Express published interest from Tottenham Hotspur.
Spanish journal MARCA, though, indicate that there is far more competition for the "must-have" player as "he is drowning in offers".
MARCA state 11 offers are on the table with those who can offer regular playing opportunities the likeliest to succeed in their bid: "Being guaranteed starter status will be a key factor when the starlet sits down to decide which offer to go for," the report stated.
MARCA also listed a number of clubs who submitted offers. They include: Borussia Dortmund, Internazionale, Juventus, Wolfsburg, Villarreal and Arsenal's Premier League rivals Manchester United.