The Portuguese was heavily linked with the Blues during the summer transfer window, but the Rossoneri refused to sell him.
The London giants were willing to pay £65m for his services, but Milan pointed towards his release clause of £131m.
Despite this, the Blues have not given up on signing Leao, and believe Milan will be tempted to sell sooner rather than later.
Leao has entered the final two years of his Rossoneri deal, and as things stand, there is an impasse in the contract talks.
Should it extend for another few months, the Milan giants could be persuaded to make a significant profit through his exit.
Chelsea could use Pulisic and Ziyech as potential makeweights to significantly lower the final transfer fee for Leao.
The Blues will have the chance to watch Leao closely when Milan face them twice in the Champions League group stage this month.