The central midfield was said to be one of 12 first-team players at the club who were told they would be allowed to move clubs this summer amid a huge squad clearout at Los Che.
The captain was perhaps the most surprising player to be named on the list, as he is still widely regarded as one of the best performers in La Liga and has shown loyalty to the club in recent years.
“I am comfortable in Valencia, it is a top city. My family, my children, they are all perfect in Valencia,” Parejo explained on Radio Marca.
“I have been at the club for nine years and for me it is my home and that is how I feel. I have two years left here and I would like to retire at Valencia because of my career.
“But football is football and you never know what is going to happen, but for me Valencia is the most important thing.”
Parejo, 31, joined Valencia from Getafe in 2011 in a €6m deal and he has amassed 383 appearances for the club, netting 64 goals in that timeframe and becoming renowned as a set-piece expert.
Jasper Cillessen, Eliaquim Mangala, Mouctar Diakhaby, Geoffrey Kondogbia, Ferran Torres, Goncalo Guedes, Ruben Sobrino, Kevin Gameiro and Rodrigo Moreno are among the other players said to be allowed to leave the Mestalla this summer.