Reports from Britain claim Valencia have approached Manuel Pellegrini with a three-year contract from next season.
Super Deporte cites the stories, which say the out-going Manchester City manager wants a long-term project for his next stop, after he is replaced by Pep Guardiola.
Pako Ayestaran is in charge at Mestalla until the end of the season after Gary Neville was sacked last week.
Pellegrini is said to have told Valencia that if he was to accept their proposal, he would want full control over the sporting department, with five signings and the run of the academy.
Zenit St Petersburg are also said to be keen on the Chilean but previous reports have said he would like to go to Valencia as he lived in the area when he had the bench at Villarreal.