The 26-year-old joined Valencia on loan last summer, with the temporary deal containing an €18m (£15.7m) option to make it permanent at the end of his season-long stay.
However, Valencia director general Mateu Alemany has admitted that the Spanish club cannot afford that price and hoped to negotiate with City in order to keep Mangala at the Mestalla.
Marca reports that City are playing hardball over the deal, though, while the player himself is also thought to support his parent club's stance of not letting him leave on the cheap.
Mangala joined City for around £32m in 2014 but played just 64 matches for the club before being shipped out upon Pep Guardiola's arrival at the Etihad Stadium last summer.
Valencia are also expected to lose fellow defenders Aymen Abdennour and Aderlan Santos this summer, while the future of loanee forward Munir El Haddadi is similarly uncertain.