The Portugal international was not called up to Roberto Martinez's squad for September fixtures against Croatia and Scotland in the UEFA Nations League and instead enjoyed an extended break without football.
Reports have since surfaced on Wednesday claiming that Nunes was involved in an altercation, during his time off, in a Spanish nightclub which resulted in the 26-year-old's arrest before being questioned at a police station.
Spanish news outlet El Mundo, via the Daily Mail, claim that Nunes's arrest took place at around 5.30am after he was accused of stealing a phone from a 58-year-old man who had attempted to take photos of him without permission in the nightclub toilets.
A spokesman for the National Police in Madrid said: 'I can confirm a Portuguese national was arrested in the early hours of September 8 at a Madrid nightclub on suspicion of stealing another person's mobile phone.'
Nunes is said to have been released a few hours later following the intervention of a lawyer, with the report adding that the midfielder is set to face charges and a trial over the incident.
Nunes will not face charges after 'exaggerated' arrest reports
However, according to the Manchester Evening News, the entire incident has been exaggerated and Nunes only pushed the phone out of the man's hand after asking him to stop taking pictures.
The report adds that police were called, but Nunes was never arrested and he will not face any further action in relation to the alleged incident.
Nunes struggled for first-team football in his debut campaign at Man City last season, but he has since made six appearance for the Citizens this term and scored his first goal for the club in a 2-1 EFL Cup win over Watford last month.
The midfielder also played the full 90 minutes in City's 4-0 Champions League win over Slovan Bratislava on Tuesday, and manager Pep Guardiola has since stressed the importance of the Portuguese in his squad this season.
Speaking to TNT Sports, Guardiola said: "We need him. We are going to play at the end of the season the [Club] World Cup with no holidays, then we start the Premier League again. We need absolutely everyone. The players don't believe it.
"Always there are players who play more minutes than the other ones. At the end in this modern football with teams playing a lot of competitions, everybody has to be ready otherwise it is impossible. They have to compete with each other and be ready for every situation."
Nunes will be hoping to force his way back into the starting lineup when Man City welcome Fulham to the Etihad Stadium for a Premier League clash on Saturday.