According to Jonathan Smith at ESPN FC, City have already had an initial bid rejected by the Serie A club, but there is confidence the two teams will be able to agree a fee for the former Liverpool man.
Should Reina arrive, it will spell bad news for Claudio Bravo, with the report noting he could now be set to leave the club, less than 12 months after his arrival from Barcelona.
City have already signed Ederson from Benfica this summer, with the 23-year-old expected to be the club's first-choice goalkeeper next season.
Per Smith, Reina could be his back-up, with Guardiola's side having bid £2.6 million although Napoli are reportedly holding out for closer to £4.4 million.
That would then leave doubts over Bravo's future, with the Chile international having come in for criticism during his debut season in England, and his failings have been highlighted by Whoscored.com:
Bravo was brought in to replace Joe Hart, who spent last season on loan at Torino and now looks set to join West Ham, per Kaveh Solhekol at Sky Sports:
Willy Caballero has also left City after his contract expired, and signed for Chelsea as a replacement for Asmir Begovic.
Whether Bravo would settle for being the club's third-choice goalkeeper remains to be seen, although Goal's Manchester City correspondent Sam Lee reported he could still remain with the club:
Guardiola's judgement of goalkeepers has been called into question after allowing Hart to leave in favour of Bravo, who subsequently failed to impress in the Premier League.
His purchase of Ederson appears to be an acknowledgement of this, and signing Reina will only strengthen that argument.
However, the City boss knows Reina well having signed him for Bayern Munich, as a back-up to Manuel Neuer in 2014.
Reina should prove a solid deputy, he has vast experience of English football, having spent almost a decade at Liverpool where he won both the FA Cup and League Cup.