The UK Sun reports that the Blues will land the England forward for £120 million.
It would be a club-record fee for Sancho, who is one of Europe’s top young players.
Chelsea are free to do business in the transfer market again, after successfully appealing against a FIFA-imposed transfer ban earlier this year.
The club could complete an agreement for Sancho in January, before loaning the 19-year-old back to Dortmund for the remainder of the campaign.