The Sky Blues have been linked with a move for the 19-year-old, who has four years left on his existing contract at his boyhood club.
It has reported recently that Sporting are not willing to part ways with their star left-back for a fee below €50 million, but City have not yet been able to match that figure for the teenager.
Additionally, it was claimed that City's pursuit of the Sintra-born full-back had reached an 'impasse', with there being claims that no concrete offers have yet been presented to his boyhood club, much due to Sporting's valuation of their teenage sensation.
The report states that Sporting are aware of the Premier League champions' interest in their academy graduate, but are in 'no rush' to sanction a sale for Mendes, owing largely to the massive interest the defender is attracting this summer.
Furthermore, the Primeira Liga champions have maintained that they will not let go of one of their most prised assets unless an offer reaching €50 million is put on the table.
Despite having their initial approach rejected, City are leading the race to sign Mendes this summer as per recent reports, but the club are biding their time in their chase of the full-back and are keeping tabs on his situation ahead of the new campaign.
With Benjamin Mendy being linked with an exit this summer, it could persuade City to raise their offer for Mendes, with Pep Guardiola and Txiki Begiristain said to be keen admirers of the defender, who amassed 35 appearances across all competitions last term.
Moreover, City are planning to raise close to £100 million before even offloading any senior players this summer, which could help them in their pursuit of Mendes.
Harry Kane and Jack Grealish remain the club's top targets for the summer, but a big-money move for Mendes cannot be ruled out as Guardiola looks to bolster his backline ahead of the 2021/22 campaign.