Cheryshev, 28, spent last season on loan at Valencia and will return to the club pending the finalisation of personal terms.
The Russia international made 23 starts in all competitions during his second short-term stay at Mestalla, notching four goals.
Copa del Rey winner Valencia will reportedly pay less than the €7 million ($11.3 million) that is said to have been the initial asking price for an outright purchase.
Cheryshev's impending move brings an end to a disappointing stint at Villarreal for the former Real Madrid winger, who starred for Russia at the 2018 FIFA World Cup.
In two seasons prior to his campaign at Valencia, he made just 11 starts in LaLiga.