The starlet who currently plys his trade at NK Adriatic Split is thought to be ready to make the step up to Premier League action.
It is believed that Roguljic has been the subject of scouting missions from several Premier League clubs, and Arsene Wenger is looking to steal a march on his rivals by tempting the Croatian to North London.
The 16-year-old attacking midfielder has made a real impression at youth level and has been likened to Real Madrid playmaker Luka Modric.
Roguljic competed for Croatia under-17s in the European qualification for Slovakia 2013, producing a number of dominant displays.
The player impressed in Croatia’s latest set of games as the under-17 side have won all three of their qualifiers with Roguljic scoring in two.
The Gunners have a proven track record of developing and nurturing young talent. It is thought that they would look to bring the player through in a similar style to the way they have with several of their youth products, the most notable being Jack Wilshere.
The trend has also emerged this campaign with both Serge Gnabry and Thomas Eisfield successfully stepping up into the first team to appear in the Capital One Cup.
However, he is not the only player from the Arsenal academy to break through into the first team in recent seasons with Francis Coquelin, and Wojciech Szczesny also graduating with flying colours, establishing themselves in the Starting XI and matchday squads.