Though Chelsea qualified for the Champions League this season, they did so with the ninth-worst defensive record in the league, and centre backs Andreas Christensen and Antonio Rüdiger have been heavily criticised for their part in the Blues' porous defence.
But while the Blues have added forwards Hakim Ziyech and Timo Werner to their squad during this summer's transfer window, they have not signed any defensive reinforcements to the side as of yet.
However, one such player they are looking at is City's Stones, according to The Mirror. The England international has been linked with a move away from the Etihad due to a lack of appearances, and City's acquisition of former Bournemouth centre back Nathan Aké has pushed him further down the pecking order.
Stones could be available for as little as £20m as the Cityzens look to cut their losses and move on from the former Everton defender.
Chelsea could also turn to another ball-playing English centre back in the form of White, who excelled on loan during Leeds' Championship title victory last season.
The Daily Star report that Chelsea could look to sell Rüdiger and replace him with White after the former yet again failed to impress in the Stamford Bridge club's 2-1 FA Cup final defeat to Arsenal.
Chelsea would not only be potentially scuppering Liverpool's plans to sign the 22-year-old centre back, but would also ruin Leeds' plans to secure their ex-loanee's services permanently.
As Sky Sports report, however, Leeds have not given up in their pursuit of White, and have just seen a £22m bid rejected for their one-time defender.
White has turned down two different contract offers with the Seagulls, who currently boast no fewer than five other established centre backs in Adam Webster, Lewis Dunk, Dan Burn, Shane Duffy and new signing Joël Veltman.
This has led to speculation that he may be looking to force his way out of his current club, with Leeds manager Marcelo Bielsa an enormous admirer of his talents.