The two midfielders were said to be among the 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.
A report earlier this week in Cadena Cope outlined how Villarreal were closing in on a deal for Parejo but it is now claimed that former Arsenal midfielder Coquelin is also on their shortlist.
That follows on from reports in Valencia-based media that Coquelin would join a club in the Middle East this summer, with it now appearing more likely he will opt to stay in Spanish football.
Coquelin has made 89 first-team appearances for Los Che since his January 2018 switch from the Gunners.
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.
It comes in the same week of reports that Villarreal will sign Real Madrid teen Takefusa Kubo on a loan deal, with the club keen to bolster their midfield following the exits of Santi Cazorla and Bruno Soriano this summer.
Jasper Cillessen, Eliaquim Mangala, Mouctar Diakhaby, Geoffrey Kondogbia, Goncalo Guedes, Ruben Sobrino, Kevin Gameiro and Rodrigo Moreno are among the other players likely to exit Valencia this summer, while Ferran Torres has already joined Manchester City.