Los Che had looked to sign the diminutive forward last summer, but the newly-rich Ligue 1 side eventually bagged their man after an impressive season for Lorient in 2010-11 when he scored 22 times in 36 league appearances.
Gameiro eventually signed to PSG for an estimated 11 million euros, but has become disenfranchised over the past 12 months, having started just nine games for Carlo Ancelotti's side.
The 25-year-old is contracted to the Parc des Princes until 2015, but with Ezequiel Lavezzi set to complete his move to PSG and the club still tracking the likes of Zlatan Ibrahimovic, the management are keen to offload Gameiro.
Valencia has been tracking the forward for the past three years, and believe the time is right to move in for the Senlis native at what should be a cut price.
Despite his nine starts last season and 24 league appearances in total, the former Lorient forward netted 10 goals for PSG in 2011-12, helping it to a respectable second-place finish in Ligue 1.