The 23-year-old is reported to be a January target for Michael Laudrup, with the Swans boss ready to dip back into the European market.
Toornstra has come to his attention after shining in the Eredivisie, with a brace in a 2-0 victory over NEC Nijmegen last Saturday seeing him bring the curtain down on the first half of the season in some style.
There is every chance that he will not be around by the time Dutch top-flight action resumes after the winter break, with a switch elsewhere a distinct possibility.
Swansea appear to be leading the chase for his signature, and Toornstra is keen to test himself in England, but until an official approach is made, the Holland U21 international is reluctant to speculate on what the future may hold.
"I really have never spoken with Swansea," he told De Telegraaf.
"But for me it is a dream to play in England at some point.
"I have had a much better season than last year. And the team is also getting better."