Silva has been in fine form this season, scoring five goals and providing two assists in 10 games for Porto.
Portuguese newspaper O Jogo claim this has alerted the Gunners who have since sent scouts to watch the 20-year-old.
Arsene Wenger is said to have been aware of the the young forward for some time, tracking him during the 2015 Under-20 World Cup in New Zealand.
Silva has since progressed from Portugal's U20 side and has earned two senior caps for his country under manager Fernando Santos.
O Jogo claim Arsenal will face competition for his signature from Premier League rivals Leicester.
The Foxes are said to have been tracking Silva for some time and have watched him in action for Porto this season.
Silva made the step up to Porto's first team towards the end of last season and spent much of the last campaign plying his trade in the Portuguese second division.
He made 29 appearances for Porto B last term, scoring 14 goals and providing three assists.