The 29 year old, who plays as an attacking midfielder, is out of contract so could sign for Swansea at any time.
He’s likely to be joined in the reserve side on Wednesday by fellow countryman Ferrie Bodde, who is set to make his comeback from a ligament injury which has kept him out since last November.
Van Dijk has played in Holland throughout his career and has had spells with 6 different clubs including Sparta Rotterdam, FC Gronigen and RKC Waalwijk.
The former Cambuur man has already been offered a contract by MLS outfit Toronto but is thought to prefer to stay in Europe.
Swansea, meanwhile, are still in negotiation with left winger Cedric van der Gun, who is also available to sign at any time after he left Utrecht in the summer.