Sanchez saw a £60m move to the Etihad Stadium collapse on deadline day because the Gunners were unable to conclude a deal for Monaco winger Thomas Lemar.
The Citizens are still confident that Sanchez wants to play under Pep Guardiola again and a renewed January bid of £20m is being prepared in the corridors of power.
City sources, however, are also hearing worrying noises that Paris have reprised their own interest and they are free to discuss a pre-contract agreement with him when the window reopens in the new year.
It is believed the loaded French outfit are willing to pay the 28-year-old an incredible £400,000 per week if he now decides to run down the rest of his contract at the Emirates Stadium, rather than opt for Manchester.
Paris, backed by the royal billions of Qatar, are already committed to £166m, next year, to make striker Kylian Mbappe’s loan move from Monaco permanent, having already parted with a world record £198m fee for Brazil superstar Neymar.
There are noises Uruguayan forward Edinson Cavani could be sold next summer to balance the books and recruiting Sanchez on a freebie is seen as an attractive proposition for PSG.