The Russian international has been heavily linked with an exit from the Estadio Mestalla in the coming weeks, with new manager Javi Gracia rumoured to be looking elsewhere for squad options.
However, according to reports from Super Deporte, Cheryshev has rejected a move to Russian club Krasnodar, as he wants to either remain at Valencia or join another top La Liga side.
Cheryshev slipped down the Los Che pecking order last season, with just nine league starts under Marcelino and Albert Celades.
The 29-year old has played his entire senior career in Spain, after coming through the youth ranks at Real Madrid, before eventually joining Villarreal in 2016.
He spent the 2018-19 campaign on loan at Valencia, before joining on a permanent €6m deal at the start of last season.