Valencia have won just once in La Liga since Prandelli took over in September and are only out of the relegation zone on goal difference.
Spanish outlet Cadena SER said the former Italy boss informed Valencia’s board of directors of his intention to resign on Friday.
The two parties will now thrash out an agreement for the termination of Prandelli’s contract before an official announcement is made.
Prandelli, 59, is the fourth manager Valencia have had in 2016 following the exits of Gary Neville, Pako Ayestaran and Salvador Gonzalez.
Prandelli is understood to have had a poor relationship with a number of Valencia’s key players, most notably Dani Parejo.
Parejo was dropped earlier in December after a video of him appearing to be drunk in a nightclub surfaced on social media.
“He hasn’t been selected and a decision will be made after the game about the video,” Prandelli said at the time. “Parejo has personally asked me for forgiveness and the whole business is stupid.”