The Brazilian international is currently under contract at the Estadio Mestalla until 2022 but wants to extend his stay at the club provided certain conditions are met.
According to reports from Marca, Los Che are only offering a further 12-month extension on the same wages, and the former Arsenal star wants an additional two years and a salary increase.
Paulista has established himself as a key player for Valencia following his arrival from the Emirates Stadium in 2017, with 93 La Liga appearances in three seasons.
The 29-year old is in the process of applying for Spanish nationality after declaring his intention to represent Spain at international level.
Paulista was called up for international duty with Brazil in 2015, however, he is yet to be capped by his native country at senior level, opening up the path to play for Spain.