The Croatian made a big impact in his native league last season, scoring 15 times and assisting three times for his team-mates in 31 matches.
Frigan, 20, finished the campaign as the second top scorer in the league, helping his Rijeka finish fourth in the table.
Sunderland are in search of a frontman and they have shortlisted and submitted a bid for the Under-21 Croatian international.
Even though the initial bid has been rejected by Rijeka, Sunderland are expected to follow up their interest in Frigan with another bid as they remain keen on signing him.
It has been claimed that the Championship outfit submitted a €4m bid for the 20-year-old striker.
All eyes will be on how Sunderland keep their interest in Frigan alive as they look to sign him.
Ross Stewart is also set to miss the opening matches of the season as he is still recovering from a ruptured Achilles.
It remains to be seen when the Black Cats will submit an improved offer for the Croat with also concrete interest from the MLS.
