The 25-year-old midfielder may find opportunities limited at the Etihad following the return of club legend Ilkay Gundogan, who arrived back in Manchester on a free transfer last week.
Nunes joined the Premier League champions last summer and has since chalked up 31 appearances across all competitions, despite failing to score a single goal for the club.
Atletico Madrid's interest in the Portuguese midfielder comes in the wake of Julian Alvarez's stunning £81million move to the Spanish capital earlier this summer.
Alvarez made his first start under Diego Simeone during Atletico's 3-0 triumph over last season's surprise package Girona on Sunday.
Atletico Madrid are considering a move for Manchester City midfielder Matheus Nunes on loan
Meanwhile, Manchester City have received a £21million offer from Al-Hilal for full-back Joao Cancelo.
Cancelo, who was once a mainstay under Pep Guardiola at the Etihad, was loaned out to Bayern Munich in January 2023 and later to Barcelona for the entirety of last season following a falling out with the Spanish manager.
Now back in Manchester and in training with the serial Premier League winners, Cancelo is weighing up the move to Al-Hilal, who are believed solely to be waiting on the Portuguese defender to accept the deal.
Barcelona also remains a possibility for the 30-year-old star, who enjoyed his time in Catalonia last term, although any offer to the Nou Camp is likely be in the form of another loan.