The Blues have been linked with the Norwegian striker but the report hints that any move for Haaland will be difficult to complete, with Kane and Lukuku both being monitored as alternatives.
The report adds that Dortmund do not want to sell the 20-year-old, especially after they let Jadon Sancho join Manchester United.
A source close to the deal has been quoted as saying: ‘Chelsea are trying but it is going to be very difficult.
‘At the moment it looks like mission impossible. It is unlikely but that doesn’t mean it can’t happen.’
The report continues and analyses the chances of either Kane or Lukuku departing their respective clubs this season.
‘Chelsea were previously considering a move for former striker Lukaku but the Belgian is keen on staying at Inter Milan,’ added the report in The Sun.
‘The Nerazzurri were expected to sell players due to financial fair play concerns but Achraf Hakimi’s sale has reportedly resolved that issue.
‘Meanwhile Spurs superstar Kane is unlikely to be allowed to make the move across London to join rivals Chelsea.’