'Sky Sports' reports that the Chilean is desperate to team up with former manager Pep Guardiola at the Etihad and would jump at the chance of a move should it arise.
Guardiola, for his part, is also keen on signing the 29-year-old, but he may wait until the summer to do so, amid concerns of upsetting the balance of his current squad, which holds an 11-point lead at the top of the Premier League table.
The aforementioned source claims that Arsenal now realise their mistake in not selling Sanchez last summer, with a deal having been agreed between the two sides, only for Arsenal to pull out at the last minute when they failed to bring in Monaco's Thomas Lemar.
Whilst Arsenal may be open to cutting their losses in January, it appears that City are content to wait it out to pick up the Arsenal star on a free at the end of the season.
Guardiola is thought to have identified three key areas for City to improve in the transfer market and carry them into the 2018/19 season, with another centre-back and back-up for Fernandinho also thought to be on the agenda.
Defenders Inigo Martinez, Virgil Van Dijk and former target Jonny Evans have all been linked with moves to the Etihad in recent weeks, whilst Borussia Dortmund midfielder Julian Weigl is also thought to be under consideration.
Are City set to form a stranglehold on English football for years to come?