Wenger tried and failed to sign the Real Madrid youngster both in the summer and again in January, but it appears it could be third time lucky for the Gunners who are looking to bolster their attacking options.
The 21 year old has failed to make any impact in the Spanish capital this season and has fallen down the pecking order with fellow academy graduate Jese now back up to Karim Benzema.
Arsenal have Olivier Giroud as their main man in attack and their current replacements for him are not of the quality that Wenger needs.
Morata would see more chance of first team football in North London than he does at present and once assured of that, the Spain under-21 international would be keen on signing a deal for the Gunners.
Madrid would demand a buy-back clause to be involved in the deal that could break the £15million barrier.