The midfielder made the move to Spain in August on loan with option to buy.
It was part of an exchange deal with similar circumstances for Joao Cancelo.
Kondogbia has made a big impression in La Liga, scoring two goals with one assist in seven appearances for Valencia.
According to reports in Spain, their decision to buy the player outright is practically made.
As part of that agreement, Inter will also retain a 30 per cent cut of any future sale Valencia make, so could continue making money on Kondogbia later on.
The Nerazzurri signed him from Monaco for €36m in the summer of 2015 after a bidding war with rivals Milan.