The Londoners were tipped to compete with Liverpool and Manchester City this term after a summer spend in excess of £220million saw them recruit Timo Werner, Kai Havertz and Ben Chilwell among others.
But a period of poor form after a 17-game unbeaten run saw Frank Lampard sacked by Roman Abramovich and replaced by Thomas Tuchel.
Chelsea have won their last three top-flight matches under the German coach but are still 11 points adrift of leaders City having played a game more than Pep Guardiola’s side.
Instead, Tuchel and co. are resigned to a battle for the Champions League spots with second-placed Manchester United six points ahead but fourth-placed Liverpool only one point above Chelsea.
The Chelsea hierarchy are already planning for next season and beyond and it is thought they could make a concerted pursuit to sign Haaland from Dortmund.
The 20-year-old Norwegian striker, who has 22 goals and six assists in 22 games this season, is available for around £67m in the summer of 2022 due to a release clause.
But The Athletic say Chelsea may make an attempt to beat the competition, which includes United and a host of other clubs, to his signature this coming summer.
Chelsea want an elite-level striker to lead their attack and see Haaland as the ideal and complete frontman to do so, but will surely face paying £100m or more to sign him this year.
Tammy Abraham and Olivier Giroud have been Chelsea’s main No 9s this term under Lampard and Tuchel with summer signing Werner, who is enduring a lengthy goal drought in the league, predominantly used as a wider forward.
And Arsenal legend and self-confessed Chelsea fan Merson says he believes it is the Stamford Bridge outfit who most need a player of Haaland’s calibre.
He told ESPN: “I can understand your interest in that question and I can understand the interest of every fan and supporter to talk about these subjects.
“I am also always a fan and interested in what is going on. But now is February. There is a long way to go.
“As you know me or maybe get to know me better, I will not talk about other players publicly when they are under contract.
“This is the kind of respect we show to them but show first of all to our players. We think about our central defenders and our strikers first and we push them to the limits.
“Everything else will be decided behind closed doors.”