The Dutch club claim that Garry Monk's side are the only team who have made their interest clear in the 21-year-old striker, who scored 14 Eredivisie goals last season
The 21-year-old striker scored 14 goals in 31 Eredivisie appearances this season and was part of Netherlands’ preliminary World Cup training camp before failing to make Louis van Gaal’s final 23-man squad.
"It's always the decision of the player, but the clubs will reach an agreement,” Munsterman told Voetbal International.
“At this moment Swansea City are the only club that made their interest clear in Castaignos."
Last week, Goal exclusively revealed that Swansea City had valued Wilfried Bony at £20 million, which influenced Liverpool’s decision to sign Rickie Lambert from Southampton ahead of the Ivorian.