The 35-year-old left Spanish giants Real Madrid after 16 years with the club, when his contract expired in June.
Ramos signed a two-year deal with PSG earlier this week, but according to Goal, the defender had several suitors for his signature.
The report states that compatriot Mikel Arteta was hoping to persuade Ramos to join Arsenal, with the North London club offering him a two-year contract worth £15m a year.
However, the experienced centre-back turned down the chance to move to the Emirates as he wanted to join a club competing in Europe.
Premier League champions Manchester City were another team interested in Ramos, with Pep Guardiola's side offering him a deal until June 2023 plus the opportunity to play for sister club New York City FC in the MLS.
Ramos instead decided to move to the French capital, where he is set to earn around £10m per year, which could rise to £13m with bonuses.