The Blues are said to have made Haaland, 20, who scored 41 goals in as many games for Dortmund last season, their top transfer target amid Tuchel’s desire to strengthen his attack.
Timo Werner endured a miserable debut season at Stamford Bridge, scoring just 12 times in 52 games, while Tammy Abraham is expected to leave after falling out of favour in the second half of the campaign.
Tuchel seemingly wants to bring in Haaland to replace them at the pinpoint of his attack, and the Daily Mail claim he will then look to add reinforcements in three other positions this summer.
Chelsea have been rock solid at the back since Tuchel replaced Frank Lampard at the end of January, conceding just 15 goals in 30 matches (five of which came when they were reduced to 10 men against West Brom).
It therefore comes as a slight surprise that the German is looking to add another centre-back to his ranks this summer, where Cesar Azpilicueta, Thiago Silva, Antonio Rudiger, Andreas Christensen and Kurt Zouma are already battling it out for three spaces in his 3-4-2-1 setup.
Fikayo Tomori is on the verge of sealing a permanent transfer to AC Milan, nevertheless, which could explain his thinking.
Reports in Germany suggest Bayern Munich defender Niklas Sule is wanted by the Blues, with the Bundesliga champions prepared to listen to offers for him, while Wolfsburg’s Maxence Lacroix and Atletico Madrid’s Jose Gimenez have also been linked with moves.
Upon arrival in west London Tuchel surprisingly used Callum Hudson-Odoi as a makeshift right wing-back, before slowly realising that Reece James is in fact his strongest option in that position.
Azpilicueta has also been used there in recent matches, but the Chelsea captain doesn’t offer enough going forward and is better suited in a back three.
Should Tuchel stick with his wing-back system next term, a more reliable backup option for James will be needed in the summer transfer window.
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The Blues are reportedly eyeing up a move for Wolves powerhouse Adama Traore, whose unparalleled physical attributes could allow him to flourish as a wing-back.
However, Tuchel could even look to his youth ranks to provide competition for James, as Chelsea’s Academy Player of the Season Tino Livramento, 18, has shown plenty of promise over the past year.
The other area Chelsea desperately need to strengthen once they’ve got their hands on a new striker is in midfield, where N’Golo Kante, Jorginho, Mateo Kovacic and Billy Gilmour are their only natural options right now.
Kante enjoyed a breathtaking season and remains a pivotal cog in the Blues wheel, yet Jorginho and Kovacic have proved too hot and cold at times, while Gilmour is still in the process of developing as a player.
Mason Mount can be used in the middle of the park, but his best form comes in one of the two attacking-midfield slots slightly further forward.
As a result, Chelsea are said to be exploring the possibility of signing a new midfielder this summer, and West Ham ace Declan Rice remains a top target.
They have also been linked with outgoing Atletico Madrid star Saul Niguez, although reports suggest he is close to joining Bayern Munich.