The 24-year-old has been told he can leave Inter Milan this summer and he is keen to sort out his future quickly.
Liverpool and Tottenham have been linked with the midfielder over the past few months and it was reported they may firm up their interest in the current transfer window.
But, according to Plaza Deportiva, Kondogbia wants to join Valencia after they opened talks with Inter.
The Spanish club are in talks over a deal for the France international that would see him join them on loan.
Inter are happy to let Kondogbia leave on a temporary basis, but they want Valencia to buy the 24-year-old outright in a year for around £16m.