Haaland has scored 43 times in as many games for Dortmund since joining the club in January last year and is one of the most wanted forwards in world football at the moment.
There are suggestions that if Dortmund fail to qualify for the Champions League, they could be forced to sell the 20-year-old in the summer transfer window.
Manchester City have identified him as a top target and Manchester United are still keen after failing to sign him last year.
But Chelsea are the ones who are believed to be keen to push the limits for Haaland and, according to German daily Bild, Tuchel has the nod of approval of the club hierarchy to chase the expensive signing of the striker.
A release clause will come into effect in Haaland’s contract in 2022 but this summer, Dortmund are likely to ask for big money.
But it seems Chelsea are prepared to push the boat out to land a player who many believe is a generational talent.
Dortmund have insisted that they are planning ahead with Haaland but it seems they will come under increasing pressure to sell him in the summer, especially if they are not in the Champions League.
Tuchel wants to add a proven striker to his squad and Haaland is believed to be Chelsea’s top target.