The 18-year-old enjoyed a stellar breakthrough campaign in the Primeira Liga last year, chipping in with one goal and one assist as Sporting lifted the top-flight title.
Mendes's form saw him rewarded with a place in Portugal's squad for Euro 2020, and his performances have supposedly caught the eye of Pep Guardiola.
However, with Portugal coach Fernando Santos keen to avoid any unwanted transfer distractions at the Euros, The Mirror reports that City have shelved their plans to sign the teenager until after the tournament.
Mendes is understood to possess a £60.1m release clause in his Sporting contract, but the report adds that Real Madrid are ready to pounce if the left-back stars at the Euros.
Chelsea and Manchester United have also been credited with an interest in Mendes, whose deal at Sporting does not expire for another four years.