According to the report, the Paraguayan striker has already agreed to join the club with Los Che sporting director Braulio Vazquez, but a fee for the transfer is yet to be finalised.
Valencia are willing to pay up to €2.5m for Valdez, but this could prove a stumbling block as the Russian outfit shelled out double that price to take him from Hercules one year ago.
Valdez has been deemed surplus to requirements following the arrival of Salomon Rondon in Kazan, and the 28-year-old and may well be heading out of the club.
The Spanish side are hopeful of completing a deal before their opening game of the new Liga season against Real Madrid next weekend.
According to the Spanish sports daily, Valencia are also actively searching for a new left-back to replace Jordi Alba, who departed for Barcelona in June.