The Netherlands U21 international, who scored 14 goals in 31 games last season, is due to have a medical and discuss personal terms with Swansea next week.
Castaignos, 21, has spent the last two seasons in the Netherlands after a short spell in Italy with Inter Milan.
He has played 11 times for the Dutch U21s, scoring five goals.
If he does join Swansea he would join forces with Wilfried Bony, who arrived from the Eredivisie last summer.
Bony was signed for a club-record £12million from Vitesse Arnhem.