The Blues have already spent over £160m on Kalidou Koulibaly , Raheem Sterling , Carney Chukwuemeka , Gabriel Slonina and Marc Cucurella this summer.
Their spending is expected to continue over the coming weeks, and according to Spanish outlet Sport, they are now aiming to land De Jong at the earliest possibility.
The Dutchman is currently reluctant to leave Barcelona, but the club are likely to sell him unless he accepts a significant pay-cut and forgoes his deferred wages.
In this case, Chelsea are in pole position to sign him ahead of United, who can't offer Champions League football. They are also willing to match his current salary.
Blues boss Thomas Tuchel has also made it a priority to sign the former Ajax graduate, and a deal could go through once Barcelona settle his outstanding salary.
Chelsea are likely to pay around £67m to secure his services this summer.