"Valencia are negotiating, and I am involved in person, with the signing in the winter transfer market," FIFA-accredited agent Francois Gallardo was quoted as saying on ESPN.
Terry, 31, is currently serving a four-match domestic ban after being found guilty of racially abusing Queens Park Rangers defender Anton Ferdinand. With Chelsea unwilling to renew his contract, the centre-back is set to move away from Stamford bridge.
"The offer is on his table. The player is out of contract in June and will not renew there for several reasons at Chelsea and he wants to come to Spain," Gallardo said.
The Blues are not willing to renew Terry's current contract as per their policies of not providing improved contracts to players above the age of 30, which would also see Frank Lampard, 34 and Ashley Cole, 31, leave the club.
Meanwhile, Valencia have already tabled an offer for 18 months with an option to extend for one more year.
"It's real. This has been going on for 15 days and two meetings have already taken place. The deal is already on his table, a year and a half plus one. I think he will accept," he said.
Terry, who is his 15th season with Chelsea, has made 546 appearances for the London club winning the Premier League thrice and the UEFA Champions League once last season. The current captain of his club also led the national side on several occasions and has 78 caps with England.