Sturgeon is a 21-year-old central midfielder, who was linked with a transfer to Liverpool just last season.
The Mirror had reported Liverpool's interest in Sturgeon last October, the Reds hoping to land him for just £2.5 million.
A month later Portuguese newspaper O Jogo reported that Chelsea had Sturgeon on their radar too, and were monitoring his progress.
Sturgeon has an English father, and while he is a Portuguese under-21 international, he remains available to play at senior level for the Three Lions.
He made 36 appearances last season for Belenenses, scoring twice and providing four assists.
A Bola report Sturgeon has caught the attention of Wednesday boss Carlos Carvalhal, who has already secured an impressive deal to sign Marco Matias, the top scoring Portuguese player in the Primeira Liga last season.
Sealing a deal for his services could be a coup for the Owls, providing their own enquiries do not stir the attention of the player's Premier League admirers.