The Daily Express says the Dutchman is believed to be close to signing a new contract in Portugal, which will see Spurs cool their interest in him.
While Spurs have been tracking his progress, Liverpool and Newcastle are also known to be keen on the Dutchman.
However, in an interview with Portuguese paper O Jogo, van Wolfswinkel's agent, Louis Laros, dismissed the speculation linking his client with a move away from Sporting.
He said: "The conversations with Sporting's directors are very advanced and I expect news in the next few weeks.
"He has still not fulfilled the challenges at Sporting and it is his desire to follow them.
"It is practically impossible he leaves in the January market."