The 19-year-old full back has impressed for the Portuguese champions, with his displays over 38 games in the top flight attracting interest from a host of European clubs.
He has been targeted by City to solve a left-back problem that has plagued Pep Guardiola since he arrived at the Etihad five years ago.
Mendes' superb campaign with Sporting saw him called up by Fernando Santos for Euro 2020, although he played understudy to Raphael Guerreiro for most of Portugal's journey.
City were to reignite their pursuit and trigger said clause, but it would see them pay way over the odds compared to the fee Sporting were initially requesting.
Mendes enjoyed a breakthrough campaign at Sporting last season, featuring in 29 of his side's 34 league outings as they were crowned Portuguese champions for the first time since 2002.
Mendes’ movement up and down the flank often allows him to recover the ball in advanced areas and set it up for his teammates to create goalscoring opportunities.
City trio Ruben Dias, Bernardo Silva and Joao Cancelo have been helping with a charm offensive to convince Mendes that he would enjoy life in the Premier League.
Manchester club have no intention of meeting Sporting's £43m valuation of Mendes and are seeking an agreement of around £25m instead.
The teenager’s energy and tenacity would suit the Premier League, where he could develop into one of the finest in his position.