The Sun reports that City boss Pep Guardiola would allow Stones to leave this summer, as the 23-year-old is currently fourth choice in central defence, following the January arrival of Aymeric Laporte.
Stones has been praised for his development under Guardiola, but the Spaniard is now keen to bring in a new centre-half this summer to compete with Vincent Kompany, Nicholas Otamendi and Laporte.
Stones joined City for £47.5million from Everton two years ago and the Premier League champions are hoping to recoup most of the fee.
The defender is earning £100,000 per week at City.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.