The English centre-back has found himself further falling down the pecking order since the arrival of Aymeric Laporte in January, having already been behind Vincent Kompany and Nicolas Otamendi.
City splurged £47.5million on the centre-half two years ago and would expect to recoup all of that fee with a sale but Guardiola is reluctantly willing to let him leave.
While he has talked up the 24-year-old regularly, Guardiola does not believe Stones has progressed enough to warrant a first-team place and he does not want to hinder the former Everton defenders development, according to the Sun.
One stumbling block in any potential sale would be the cost of the deal for other clubs.
While Stones is keen to leave in search of first-team football, most teams would struggle to finance a move.
Arsenal are thought to be keen to land him, but are expected to only have a transfer budget of £50m.
With Stones commanding £100,000-a-week, he may be out of their price range.
Liverpool do have money to spend after selling Philippe Coutinho to Barcelona for £145m in January and Jurgen Klopp is believed to be a fan.
More: Arsenal FC