The Blues have earmarked the Norway international at the top of their transfer target list, the PA news agency understands.
According to reports in Germany last week, the Norwegian would only consider a move to six clubs, with Chelsea not on that list.
The 20-year-old has a clause in his BVB contract that would force the club to accept a fee of £66m in 2022.
The financial impact of COVID have left Dortmund seriously considering cashing in on the youngster this summer.
Haaland has enjoyed an impressive 2020-21 campaign for Dortmund, scoring 29 goals in 28 matches in all competitions.