The 20-year-old, who has been selected in the Greece squad for the World Cup, was the subject of a bid from Napoli last season.
Forest are said to be exploring several options in case a Premier League club makes a move for goalkeeper Karl Darlow.
According to the Nottingham Post, the Championship outfit have been scouting Kapino as a potential replacement for the stopper.
It is thought that a bid in the region of £2.5m would be enough to persuade Panathinaikos to sell.
Kapino has made 50 appearances for the Greek club.