The 20-year-old scored 41 goals in 41 appearances for BVB during the 2020-21 campaign and is believed to be wanted by a number of leading clubs in European football.
Barcelona, Real Madrid, Manchester United, Manchester City and Chelsea are all thought to be in the running to sign the Norway international, who will have a buy-out clause in his Dortmund contract next year.
According to journalist Ian McGarry, speaking on The Transfer Window podcast, Chelsea have already come to an agreement with the Norway international over personal terms.
However, the Blues are yet to settle on a transfer fee with Dortmund, who are believed to have placed a £172m asking price on the youngster during this summer's transfer window.
"Personal terms for Haaland are signed off. It's just a case of Chelsea agreeing a fee with Dortmund," said McGarry.
The Norwegian, who is believed to favour a move to Real Madrid, has scored 57 goals in 59 appearances for his German club since arriving from Red Bull Salzburg in January 2020. body check tags ::