To do that, they must bridge a huge gap to Manchester City and Liverpool – last season’s top-two finishers.
The business so far has been very positive, and if reports are to be believed, then it looks like they’re about to sign a seventh new player.
Find out who that is below, as we have gathered the latest rumours on Chelsea.
Mendy deal ‘done’
Mendy will come to Stamford Bridge to provide some competition for Kepa Arrizabalaga, who has been heavily criticised recently.
The French media are claiming the fee will be around €28m for the 28-year-old shot-stopper, who impressed in Ligue 1 last season.
Rennes wanted more for Mendy, but with the goalkeeper so keen for a move to England, they have compromised with the Blues.
PSG chase Blues midfielder
The report claims that PSG are back in for Bakayoko, after previously being interested in the Frenchman.
The 26-year-old spent last season out on loan at Monaco and does not appear to be in Frank Lampard’s plans.
Bakayoko is reportedly interested in moving back to AC Milan, where he had a spell on loan two years ago, but the Serie A giants are not able to suit his wage demands.
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Inter still interested in Kante
Antonio Conte’s Inter Milan will have to sell some players in order to find the funds to sign Chelsea star N’Golo Kante.
That’s according to Milan-based newspaper Gazzetta dello Sport, who claim that Joao Mario and Radja Nainggolan are “unneeded” at the San Siro and could be sold.
Former Blues boss Conte has identified the Frenchman as his top target this summer, but they will need to work on their outgoings before they can think about signing the 29-year-old.
Chelsea are asking for around €50m for Kante, who played the full 90 minutes in the side’s 3-1 win over Brighton & Hove Albion last week.