The 31-year-old was recently banned for racially abusing Anton Ferdinand last October and was also given a fine by his club for the incident.
Valencia believe that the situation may have unsettled Terry and FIFA agent Francois Gallardo insists that a deal between the two parties is a possibility.
Gallardo told Radio Intereconomia: "Terry has problems. They are insulting him and he is not taking it anymore. He asked to leave, not us.
"It's real. This has been going on for 15 days and two meetings have already took place. The deal is already on his table - a year and a half plus one.
"I think he will accept."
Terry captained Chelsea to a 2-1 loss against Shakhtar Donetsk in the Champions League on Tuesday evening.