The Chilean, who will be replaced by Pep Guardiola at the Etihad Stadium next summer, wants a greater show of commitment from the Russian Premier League side.
Manchester City manager Manuel Pellegrini has been offered a two-year contract by Zenit St. Petersburg, but is holding out for a longer deal as he plots the final years of his managerial career, a source tells Goal UK.
Goal UK understands Zenit has moved ahead of Valencia and an undisclosed Italian club as it looks to replace Andre Villas-Boas, who has already announced his decision to step down at the end of the season.