The Blues have moved to rival Newcastle United to sign the 21-year-old winger, the PA news agency understands.
Chelsea are thought to be in negotiations with the Toffees over a permanent switch for the England U-21 international.
The Merseyside outfit are hopeful of pushing for £50m to allow Gordon to leave Goodison Park.
Chelsea owners Todd Boehly and Clearlake Capital have already spent big on Raheem Sterling, Kalidou Koulibaly, Marc Cucurella and Carney Chukwuemeka so far this summer.
Highly promising young shot-stopper Gabriel Slonina has been signed and set to remain on loan at Chicago Fire, while the West Londoners continue to chase Inter Milan’s midfielder Cesare Casadei.
Chelsea boss Thomas Tuchel are understood to be in negotiations with the Catalan giants Barcelona over a deal for Pierre-Emerick Aubameyang, while the hunt to lure Wesley Fofana to Stamford Bridge also continues.