Amid talk of a switch to Steve McClaren's side, the Swans boss has insisted his midfielder wants to remain at the Liberty Stadium
Shelvey was in the starting XI on Sunday as Swansea crashed out of the FA Cup third round with a shock 3-2 loss to League Two side Oxford United.
The midfielder has fallen out of favour at the Liberty Stadium and reports have suggested Newcastle are hoping to agree a £10million deal for the England international.
Shelvey was also reported to have become involved in an altercation with supporters following the final whistle, but Curtis insists he is not looking to move on.
He told Sky Sports: "There's always speculation.
"Because he's not in the Premiership side and he's an England international, there's always going to be speculation about Jonjo. He wants to stay."
Swansea took the lead at the Kassam Stadium thanks to Jefferson Montero's 23rd-minute strike.
Yet a Liam Sercombe penalty and a brace for Kemar Roofe sealed a win for Oxford and Curtis admits an early exit may help his side's attempts to avoid relegation from the top-flight.
Asked if their exit was a blessing in disguise for his relegation-threatened side, Curtis said: "Well it could be, I've got to be honest I'd love to have gone a little bit further. It just breeds confidence.
"Some of them probably lack a bit of match hardness. [It was] disappointing, we have to do better."