Los Che are understood to be closing in on the Portuguese full-back, who has been coy when asked about his future at the Estadio de Alvalade
The Portugal international, who joined the club from Sporting Braga in 2009 in a €3 million deal, has been linked with a new challenge after becoming an integral part of Ricardo Sa Pinto's side.
It is believed that new Valencia coach Mauricio Pellegrino has made the signing of a new right-sided defender his top priority, with Los Che willing to offer €5m for the Portuguese.
Questioned about his future at the weekend, the 28-year-old told reporters: "I am not thinking about my future just yet. I want what is best for me and for Sporting."
Pereira, who began his career at Benfica, has been included in Portugal's 23-man squad for Euro 2012.