The 23-year-old has attracted interest from across Europe, including Manchester United.
Spurs sent a scout to watch the Dutchman during Monday's Lisbon derby at the Estadio Jose Avalade, according to A Bola.
Van Wolfswinkel is believed to have a €22m (£18m) release clause in his contract with the Portuguese club.
However, his agent has claimed that the forward could be signed for a lot less over the summer.
The former Utrecht player is contracted with Lisbon until 2016.