The three European giants have all taken an interest in Ramos' situation after it was confirmed that the veteran defender would leave Real Madrid on June 30 on a free transfer when his contract expires.
The 35-year-old is now weighing up the pros and cons of each option, sources said, with family considerations being an important factor in his decision-making.
ESPN reported last month that City were considering making Ramos an offer if he did not reach a renewal agreement with Madrid.
That interest persists, and the Premier League club would be willing to offer Ramos a two-year contract which would be reassessed in the summer of 2023.
At that point, depending on the centre-back's performance and priorities, Ramos could stay at City for a third season, or move to the United States to play for City Group's Major League Soccer franchise New York City FC.
Sources told ESPN that City manager Pep Guardiola believes a defender with Ramos' experience would complement the younger options already in City's squad such as Ruben Dias, 24, John Stones, 27, Nathan Ake, 26, and Aymeric Laporte, 27.
City would give Ramos the chance to play for a club competing to win the Champions League, which is one of his priorities, although sources told ESPN there were some concerns about the impact on his family of a move to Manchester.
At the same time, PSG's interest has grown since Ramos announced his departure from Madrid.
Sources told ESPN that there had been some informal discussions between Ramos' camp and PSG last season, but the French club had not wanted to make that interest concrete until Ramos' Madrid exit became official.
PSG had believed the defender would end up renewing, sources said, but since his future became clear, contact had been made by the club's sporting director Leonardo.
The role of coach Mauricio Pochettino -- a long-term fan of Ramos -- is also thought to be important, believing his leadership qualities would help avoid a repeat of last year's disappointments in Ligue 1 and the Champions League.
Signing a centre-back is not a priority for PSG this summer with Presnel Kimpembe, Marquinhos, Abdou Diallo and Thilo Kehrer already at Pochettino's disposal, but sources told ESPN signing a player of Ramos' quality on a free transfer would be considered a market opportunity.
The latest team to express an interest in Ramos is Bayern, ESPN has been told.
The Bundesliga club have already signed Dayot Upamecano and have Niklas Sule and youngster Tanguy Nianzou at the disposal of new coach Julian Nagelsmann but are expected to look for an experienced alternative to replace the departing David Alaba and Jerome Boateng.
A move for Ramos to Germany would be seen as difficult, if not impossible, however, given concerns over his adaptation and the language barrier.
Ramos is still considering his options but is keen to resolve his future sooner rather than later, sources added, and does not want to delay a decision too long out of respect for the clubs which have expressed an interest.