The source claims that Arsene Wenger himself called the Spanish club in September to enquire about the availability of the talented forward.
Real Madrid’s response was negative, but the Gunners still hope they can persuade the player that his future lies at the Emirates.
Morata is held in high regard by the club officials and boss Jose Mourinho and he was handed a first team debut almost two years ago.
However, the 20-year-old has since been a victim of fierce competition for places at Santiago Bernabeu and made just three more substitute appearances for los Blancos.
Morata, who is currently part of Spain Under-21 side, has scored a total of 33 goals in 68 league appearances for Real Madrid Castilla.
He has been struggling to find his scoring boots this term, netting just twice in five league games.